diff --git a/Library/Homebrew/download_strategy.rb b/Library/Homebrew/download_strategy.rb
index 7d8465048a..de269d55eb 100644
--- a/Library/Homebrew/download_strategy.rb
+++ b/Library/Homebrew/download_strategy.rb
@@ -47,8 +47,11 @@ class AbstractDownloadStrategy
   # chdir into the newly-unpacked directory.
   # Unlike {Resource#stage}, this does not take a block.
   def stage
-    UnpackStrategy.detect(cached_location, ref_type: @ref_type, ref: @ref)
+    UnpackStrategy.detect(cached_location,
+                          extension_only: true,
+                          ref_type: @ref_type, ref: @ref)
                   .extract_nestedly(basename: basename_without_params,
+                                    extension_only: true,
                                     verbose: ARGV.verbose? && !shutup)
   end
 
diff --git a/Library/Homebrew/unpack_strategy.rb b/Library/Homebrew/unpack_strategy.rb
index 154724ec0a..d4068963f3 100644
--- a/Library/Homebrew/unpack_strategy.rb
+++ b/Library/Homebrew/unpack_strategy.rb
@@ -1,36 +1,60 @@
 module UnpackStrategy
-  # length of the longest regex (currently Tar)
-  MAX_MAGIC_NUMBER_LENGTH = 262
-  private_constant :MAX_MAGIC_NUMBER_LENGTH
+  module Magic
+    # length of the longest regex (currently Tar)
+    MAX_MAGIC_NUMBER_LENGTH = 262
+
+    refine Pathname do
+      def magic_number
+        @magic_number ||= if directory?
+          ""
+        else
+          binread(MAX_MAGIC_NUMBER_LENGTH) || ""
+        end
+      end
+
+      def file_type
+        @file_type ||= system_command("file", args: ["-b", self], print_stderr: false)
+                       .stdout.chomp
+      end
+
+      def zipinfo
+        @zipinfo ||= system_command("zipinfo", args: ["-1", self], print_stderr: false)
+                     .stdout
+                     .encode(Encoding::UTF_8, invalid: :replace)
+                     .split("\n")
+      end
+    end
+  end
+  private_constant :Magic
 
   def self.strategies
     @strategies ||= [
-      Pkg,
-      Ttf,
-      Otf,
-      Air,
-      Executable,
-      SelfExtractingExecutable,
-      Jar,
-      LuaRock,
-      MicrosoftOfficeXml,
-      Zip,
-      Dmg,
-      Xar,
-      Compress,
-      Tar,
-      Bzip2,
+      Tar, # needs to be before Bzip2/Gzip/Xz/Lzma
       Gzip,
       Lzma,
       Xz,
       Lzip,
+      Air, # needs to be before Zip
+      Jar, # needs to be before Zip
+      LuaRock, # needs to be before Zip
+      MicrosoftOfficeXml, # needs to be before Zip
+      Zip,
+      Pkg, # needs to be before Xar
+      Xar,
+      Ttf,
+      Otf,
       Git,
       Mercurial,
       Subversion,
       Cvs,
+      SelfExtractingExecutable, # needs to be before Cab
+      Cab,
+      Executable,
+      Dmg, # needs to be before Bzip2
+      Bzip2,
       Fossil,
       Bazaar,
-      Cab,
+      Compress,
       P7Zip,
       Sit,
       Rar,
@@ -42,6 +66,7 @@ module UnpackStrategy
   def self.from_type(type)
     type = {
       naked: :uncompressed,
+      nounzip: :uncompressed,
       seven_zip: :p7zip,
     }.fetch(type, type)
 
@@ -52,32 +77,30 @@ module UnpackStrategy
     end
   end
 
-  def self.from_path(path)
-    magic_number = if path.directory?
-      ""
-    else
-      File.binread(path, MAX_MAGIC_NUMBER_LENGTH) || ""
-    end
-
-    strategy = strategies.detect do |s|
-      s.can_extract?(path: path, magic_number: magic_number)
-    end
-
-    # This is so that bad files produce good error messages.
-    strategy ||= case path.extname
-    when ".tar", ".tar.gz", ".tgz", ".tar.bz2", ".tbz", ".tar.xz", ".txz"
-      Tar
-    when ".zip"
-      Zip
-    else
-      Uncompressed
-    end
-
-    strategy
+  def self.from_extension(extension)
+    strategies.sort_by { |s| s.extensions.map(&:length).max(0) }
+              .reverse
+              .detect { |s| s.extensions.any? { |ext| extension.end_with?(ext) } }
   end
 
-  def self.detect(path, type: nil, ref_type: nil, ref: nil)
-    strategy = type ? from_type(type) : from_path(path)
+  def self.from_magic(path)
+    strategies.detect { |s| s.can_extract?(path) }
+  end
+
+  def self.detect(path, extension_only: false, type: nil, ref_type: nil, ref: nil)
+    strategy = from_type(type) if type
+
+    if extension_only
+      strategy ||= from_extension(path.extname)
+      strategy ||= strategies.select { |s| s < Directory || s == Fossil }
+                             .detect { |s| s.can_extract?(path) }
+    else
+      strategy ||= from_magic(path)
+      strategy ||= from_extension(path.extname)
+    end
+
+    strategy ||= Uncompressed
+
     strategy.new(path, ref_type: ref_type, ref: ref)
   end
 
@@ -96,7 +119,7 @@ module UnpackStrategy
     extract_to_dir(unpack_dir, basename: basename, verbose: verbose)
   end
 
-  def extract_nestedly(to: nil, basename: nil, verbose: false)
+  def extract_nestedly(to: nil, basename: nil, verbose: false, extension_only: false)
     Dir.mktmpdir do |tmp_unpack_dir|
       tmp_unpack_dir = Pathname(tmp_unpack_dir)
 
@@ -105,9 +128,9 @@ module UnpackStrategy
       children = tmp_unpack_dir.children
 
       if children.count == 1 && !children.first.directory?
-        s = UnpackStrategy.detect(children.first)
+        s = UnpackStrategy.detect(children.first, extension_only: extension_only)
 
-        s.extract_nestedly(to: to, verbose: verbose)
+        s.extract_nestedly(to: to, verbose: verbose, extension_only: extension_only)
         next
       end
 
diff --git a/Library/Homebrew/unpack_strategy/air.rb b/Library/Homebrew/unpack_strategy/air.rb
index 4fd819c888..1b12e221b0 100644
--- a/Library/Homebrew/unpack_strategy/air.rb
+++ b/Library/Homebrew/unpack_strategy/air.rb
@@ -2,8 +2,15 @@ module UnpackStrategy
   class Air
     include UnpackStrategy
 
-    def self.can_extract?(path:, magic_number:)
-      path.extname == ".air"
+    using Magic
+
+    def self.extensions
+      [".air"]
+    end
+
+    def self.can_extract?(path)
+      mime_type = "application/vnd.adobe.air-application-installer-package+zip"
+      path.magic_number.match?(/.{59}#{Regexp.escape(mime_type)}/)
     end
 
     def dependencies
diff --git a/Library/Homebrew/unpack_strategy/bazaar.rb b/Library/Homebrew/unpack_strategy/bazaar.rb
index 4811d27279..684a5cad28 100644
--- a/Library/Homebrew/unpack_strategy/bazaar.rb
+++ b/Library/Homebrew/unpack_strategy/bazaar.rb
@@ -2,7 +2,9 @@ require_relative "directory"
 
 module UnpackStrategy
   class Bazaar < Directory
-    def self.can_extract?(path:, magic_number:)
+    using Magic
+
+    def self.can_extract?(path)
       super && (path/".bzr").directory?
     end
 
diff --git a/Library/Homebrew/unpack_strategy/bzip2.rb b/Library/Homebrew/unpack_strategy/bzip2.rb
index 60378b7003..e47cc062df 100644
--- a/Library/Homebrew/unpack_strategy/bzip2.rb
+++ b/Library/Homebrew/unpack_strategy/bzip2.rb
@@ -2,8 +2,14 @@ module UnpackStrategy
   class Bzip2
     include UnpackStrategy
 
-    def self.can_extract?(path:, magic_number:)
-      magic_number.match?(/\ABZh/n)
+    using Magic
+
+    def self.extensions
+      [".bz2"]
+    end
+
+    def self.can_extract?(path)
+      path.magic_number.match?(/\ABZh/n)
     end
 
     private
diff --git a/Library/Homebrew/unpack_strategy/cab.rb b/Library/Homebrew/unpack_strategy/cab.rb
index acc3b1ec32..afbf9e3784 100644
--- a/Library/Homebrew/unpack_strategy/cab.rb
+++ b/Library/Homebrew/unpack_strategy/cab.rb
@@ -2,8 +2,14 @@ module UnpackStrategy
   class Cab
     include UnpackStrategy
 
-    def self.can_extract?(path:, magic_number:)
-      magic_number.match?(/\AMSCF/n)
+    using Magic
+
+    def self.extensions
+      [".cab"]
+    end
+
+    def self.can_extract?(path)
+      path.magic_number.match?(/\AMSCF/n)
     end
 
     def extract_to_dir(unpack_dir, basename:, verbose:)
diff --git a/Library/Homebrew/unpack_strategy/compress.rb b/Library/Homebrew/unpack_strategy/compress.rb
index a1851ccf4d..952e17c980 100644
--- a/Library/Homebrew/unpack_strategy/compress.rb
+++ b/Library/Homebrew/unpack_strategy/compress.rb
@@ -2,8 +2,14 @@ require_relative "tar"
 
 module UnpackStrategy
   class Compress < Tar
-    def self.can_extract?(path:, magic_number:)
-      magic_number.match?(/\A\037\235/n)
+    using Magic
+
+    def self.extensions
+      [".compress"]
+    end
+
+    def self.can_extract?(path)
+      path.magic_number.match?(/\A\037\235/n)
     end
   end
 end
diff --git a/Library/Homebrew/unpack_strategy/cvs.rb b/Library/Homebrew/unpack_strategy/cvs.rb
index cca3010703..4ec2b03c23 100644
--- a/Library/Homebrew/unpack_strategy/cvs.rb
+++ b/Library/Homebrew/unpack_strategy/cvs.rb
@@ -2,7 +2,9 @@ require_relative "directory"
 
 module UnpackStrategy
   class Cvs < Directory
-    def self.can_extract?(path:, magic_number:)
+    using Magic
+
+    def self.can_extract?(path)
       super && (path/"CVS").directory?
     end
   end
diff --git a/Library/Homebrew/unpack_strategy/directory.rb b/Library/Homebrew/unpack_strategy/directory.rb
index 540369de75..5aa39e9137 100644
--- a/Library/Homebrew/unpack_strategy/directory.rb
+++ b/Library/Homebrew/unpack_strategy/directory.rb
@@ -2,7 +2,13 @@ module UnpackStrategy
   class Directory
     include UnpackStrategy
 
-    def self.can_extract?(path:, magic_number:)
+    using Magic
+
+    def self.extensions
+      []
+    end
+
+    def self.can_extract?(path)
       path.directory?
     end
 
diff --git a/Library/Homebrew/unpack_strategy/dmg.rb b/Library/Homebrew/unpack_strategy/dmg.rb
index 1068c93486..b15ec3c44d 100644
--- a/Library/Homebrew/unpack_strategy/dmg.rb
+++ b/Library/Homebrew/unpack_strategy/dmg.rb
@@ -4,6 +4,8 @@ module UnpackStrategy
   class Dmg
     include UnpackStrategy
 
+    using Magic
+
     module Bom
       DMG_METADATA = Set.new %w[
         .background
@@ -83,12 +85,18 @@ module UnpackStrategy
           end
 
           system_command! "ditto", args: ["--bom", bomfile.path, "--", path, unpack_dir]
+
+          FileUtils.chmod "u+w", Pathname.glob(unpack_dir/"**/*").reject(&:symlink?)
         end
       end
     end
     private_constant :Mount
 
-    def self.can_extract?(path:, magic_number:)
+    def self.extensions
+      [".dmg"]
+    end
+
+    def self.can_extract?(path)
       imageinfo = system_command("hdiutil",
                                  args: ["imageinfo", path],
                                  print_stderr: false).stdout
diff --git a/Library/Homebrew/unpack_strategy/executable.rb b/Library/Homebrew/unpack_strategy/executable.rb
index 020a86b99f..3378bb6ff1 100644
--- a/Library/Homebrew/unpack_strategy/executable.rb
+++ b/Library/Homebrew/unpack_strategy/executable.rb
@@ -2,8 +2,15 @@ require_relative "uncompressed"
 
 module UnpackStrategy
   class Executable < Uncompressed
-    def self.can_extract?(path:, magic_number:)
-      magic_number.match?(/\A#!\s*\S+/n)
+    using Magic
+
+    def self.extensions
+      [".sh", ".bash"]
+    end
+
+    def self.can_extract?(path)
+      path.magic_number.match?(/\A#!\s*\S+/n) ||
+        path.magic_number.match?(/\AMZ/n)
     end
   end
 end
diff --git a/Library/Homebrew/unpack_strategy/fossil.rb b/Library/Homebrew/unpack_strategy/fossil.rb
index 49b480ceab..5bc5e5e78f 100644
--- a/Library/Homebrew/unpack_strategy/fossil.rb
+++ b/Library/Homebrew/unpack_strategy/fossil.rb
@@ -2,8 +2,14 @@ module UnpackStrategy
   class Fossil
     include UnpackStrategy
 
-    def self.can_extract?(path:, magic_number:)
-      return false unless magic_number.match?(/\ASQLite format 3\000/n)
+    using Magic
+
+    def self.extensions
+      []
+    end
+
+    def self.can_extract?(path)
+      return false unless path.magic_number.match?(/\ASQLite format 3\000/n)
 
       # Fossil database is made up of artifacts, so the `artifact` table must exist.
       query = "select count(*) from sqlite_master where type = 'view' and name = 'artifact'"
diff --git a/Library/Homebrew/unpack_strategy/generic_unar.rb b/Library/Homebrew/unpack_strategy/generic_unar.rb
index 3b11df94a4..f9e65b9dec 100644
--- a/Library/Homebrew/unpack_strategy/generic_unar.rb
+++ b/Library/Homebrew/unpack_strategy/generic_unar.rb
@@ -2,7 +2,13 @@ module UnpackStrategy
   class GenericUnar
     include UnpackStrategy
 
-    def self.can_extract?(path:, magic_number:)
+    using Magic
+
+    def self.extensions
+      []
+    end
+
+    def self.can_extract?(_path)
       false
     end
 
diff --git a/Library/Homebrew/unpack_strategy/git.rb b/Library/Homebrew/unpack_strategy/git.rb
index 2f9f6668b1..2f5768ca54 100644
--- a/Library/Homebrew/unpack_strategy/git.rb
+++ b/Library/Homebrew/unpack_strategy/git.rb
@@ -2,7 +2,9 @@ require_relative "directory"
 
 module UnpackStrategy
   class Git < Directory
-    def self.can_extract?(path:, magic_number:)
+    using Magic
+
+    def self.can_extract?(path)
       super && (path/".git").directory?
     end
   end
diff --git a/Library/Homebrew/unpack_strategy/gzip.rb b/Library/Homebrew/unpack_strategy/gzip.rb
index 6ae5517603..d575721d74 100644
--- a/Library/Homebrew/unpack_strategy/gzip.rb
+++ b/Library/Homebrew/unpack_strategy/gzip.rb
@@ -2,8 +2,14 @@ module UnpackStrategy
   class Gzip
     include UnpackStrategy
 
-    def self.can_extract?(path:, magic_number:)
-      magic_number.match?(/\A\037\213/n)
+    using Magic
+
+    def self.extensions
+      [".gz"]
+    end
+
+    def self.can_extract?(path)
+      path.magic_number.match?(/\A\037\213/n)
     end
 
     private
diff --git a/Library/Homebrew/unpack_strategy/jar.rb b/Library/Homebrew/unpack_strategy/jar.rb
index 35e2b211c0..90d4f6485c 100644
--- a/Library/Homebrew/unpack_strategy/jar.rb
+++ b/Library/Homebrew/unpack_strategy/jar.rb
@@ -2,14 +2,17 @@ require_relative "uncompressed"
 
 module UnpackStrategy
   class Jar < Uncompressed
-    def self.can_extract?(path:, magic_number:)
-      return false unless Zip.can_extract?(path: path, magic_number: magic_number)
+    using Magic
+
+    def self.extensions
+      [".apk", ".jar"]
+    end
+
+    def self.can_extract?(path)
+      return false unless Zip.can_extract?(path)
 
       # Check further if the ZIP is a JAR/WAR.
-      out, = Open3.capture3("zipinfo", "-1", path)
-      out.encode(Encoding::UTF_8, invalid: :replace)
-         .split("\n")
-         .include?("META-INF/MANIFEST.MF")
+      path.zipinfo.include?("META-INF/MANIFEST.MF")
     end
   end
 end
diff --git a/Library/Homebrew/unpack_strategy/lha.rb b/Library/Homebrew/unpack_strategy/lha.rb
index 9f71e75613..b3671b0a60 100644
--- a/Library/Homebrew/unpack_strategy/lha.rb
+++ b/Library/Homebrew/unpack_strategy/lha.rb
@@ -2,8 +2,14 @@ module UnpackStrategy
   class Lha
     include UnpackStrategy
 
-    def self.can_extract?(path:, magic_number:)
-      magic_number.match?(/\A..-(lh0|lh1|lz4|lz5|lzs|lh\\40|lhd|lh2|lh3|lh4|lh5)-/n)
+    using Magic
+
+    def self.extensions
+      [".lha", ".lzh"]
+    end
+
+    def self.can_extract?(path)
+      path.magic_number.match?(/\A..-(lh0|lh1|lz4|lz5|lzs|lh\\40|lhd|lh2|lh3|lh4|lh5)-/n)
     end
 
     def dependencies
diff --git a/Library/Homebrew/unpack_strategy/lua_rock.rb b/Library/Homebrew/unpack_strategy/lua_rock.rb
index d9a9c2e6ba..fe3d8f130b 100644
--- a/Library/Homebrew/unpack_strategy/lua_rock.rb
+++ b/Library/Homebrew/unpack_strategy/lua_rock.rb
@@ -2,14 +2,17 @@ require_relative "uncompressed"
 
 module UnpackStrategy
   class LuaRock < Uncompressed
-    def self.can_extract?(path:, magic_number:)
-      return false unless Zip.can_extract?(path: path, magic_number: magic_number)
+    using Magic
+
+    def self.extensions
+      [".rock"]
+    end
+
+    def self.can_extract?(path)
+      return false unless Zip.can_extract?(path)
 
       # Check further if the ZIP is a LuaRocks package.
-      out, = Open3.capture3("zipinfo", "-1", path)
-      out.encode(Encoding::UTF_8, invalid: :replace)
-         .split("\n")
-         .any? { |line| line.match?(%r{\A[^/]+.rockspec\Z}) }
+      path.zipinfo.grep(%r{\A[^/]+.rockspec\Z}).any?
     end
   end
 end
diff --git a/Library/Homebrew/unpack_strategy/lzip.rb b/Library/Homebrew/unpack_strategy/lzip.rb
index 21200c556d..f96e0ab2da 100644
--- a/Library/Homebrew/unpack_strategy/lzip.rb
+++ b/Library/Homebrew/unpack_strategy/lzip.rb
@@ -2,8 +2,14 @@ module UnpackStrategy
   class Lzip
     include UnpackStrategy
 
-    def self.can_extract?(path:, magic_number:)
-      magic_number.match?(/\ALZIP/n)
+    using Magic
+
+    def self.extensions
+      [".lz"]
+    end
+
+    def self.can_extract?(path)
+      path.magic_number.match?(/\ALZIP/n)
     end
 
     def dependencies
diff --git a/Library/Homebrew/unpack_strategy/lzma.rb b/Library/Homebrew/unpack_strategy/lzma.rb
index f759b0cb66..a9a60a0b9a 100644
--- a/Library/Homebrew/unpack_strategy/lzma.rb
+++ b/Library/Homebrew/unpack_strategy/lzma.rb
@@ -2,8 +2,14 @@ module UnpackStrategy
   class Lzma
     include UnpackStrategy
 
-    def self.can_extract?(path:, magic_number:)
-      magic_number.match?(/\A\]\000\000\200\000/n)
+    using Magic
+
+    def self.extensions
+      [".lzma"]
+    end
+
+    def self.can_extract?(path)
+      path.magic_number.match?(/\A\]\000\000\200\000/n)
     end
 
     def extract_to_dir(unpack_dir, basename:, verbose:)
diff --git a/Library/Homebrew/unpack_strategy/mercurial.rb b/Library/Homebrew/unpack_strategy/mercurial.rb
index 518878fdb2..34e897857c 100644
--- a/Library/Homebrew/unpack_strategy/mercurial.rb
+++ b/Library/Homebrew/unpack_strategy/mercurial.rb
@@ -2,7 +2,9 @@ require_relative "directory"
 
 module UnpackStrategy
   class Mercurial < Directory
-    def self.can_extract?(path:, magic_number:)
+    using Magic
+
+    def self.can_extract?(path)
       super && (path/".hg").directory?
     end
 
diff --git a/Library/Homebrew/unpack_strategy/microsoft_office_xml.rb b/Library/Homebrew/unpack_strategy/microsoft_office_xml.rb
index 6f3501816f..50647869e2 100644
--- a/Library/Homebrew/unpack_strategy/microsoft_office_xml.rb
+++ b/Library/Homebrew/unpack_strategy/microsoft_office_xml.rb
@@ -2,12 +2,22 @@ require_relative "uncompressed"
 
 module UnpackStrategy
   class MicrosoftOfficeXml < Uncompressed
-    def self.can_extract?(path:, magic_number:)
-      return false unless Zip.can_extract?(path: path, magic_number: magic_number)
+    using Magic
+
+    def self.extensions
+      [
+        ".doc", ".docx",
+        ".ppt", ".pptx",
+        ".xls", ".xlsx"
+      ]
+    end
+
+    def self.can_extract?(path)
+      return false unless Zip.can_extract?(path)
 
       # Check further if the ZIP is a Microsoft Office XML document.
-      magic_number.match?(/\APK\003\004/n) &&
-        magic_number.match?(%r{\A.{30}(\[Content_Types\]\.xml|_rels/\.rels)}n)
+      path.magic_number.match?(/\APK\003\004/n) &&
+        path.magic_number.match?(%r{\A.{30}(\[Content_Types\]\.xml|_rels/\.rels)}n)
     end
   end
 end
diff --git a/Library/Homebrew/unpack_strategy/otf.rb b/Library/Homebrew/unpack_strategy/otf.rb
index f8f4ee531f..a540f7779f 100644
--- a/Library/Homebrew/unpack_strategy/otf.rb
+++ b/Library/Homebrew/unpack_strategy/otf.rb
@@ -2,8 +2,14 @@ require_relative "uncompressed"
 
 module UnpackStrategy
   class Otf < Uncompressed
-    def self.can_extract?(path:, magic_number:)
-      magic_number.match?(/\AOTTO/n)
+    using Magic
+
+    def self.extensions
+      [".otf"]
+    end
+
+    def self.can_extract?(path)
+      path.magic_number.match?(/\AOTTO/n)
     end
   end
 end
diff --git a/Library/Homebrew/unpack_strategy/p7zip.rb b/Library/Homebrew/unpack_strategy/p7zip.rb
index 4a8d7d093b..cfb76d08c9 100644
--- a/Library/Homebrew/unpack_strategy/p7zip.rb
+++ b/Library/Homebrew/unpack_strategy/p7zip.rb
@@ -2,8 +2,14 @@ module UnpackStrategy
   class P7Zip
     include UnpackStrategy
 
-    def self.can_extract?(path:, magic_number:)
-      magic_number.match?(/\A7z\xBC\xAF\x27\x1C/n)
+    using Magic
+
+    def self.extensions
+      [".7z"]
+    end
+
+    def self.can_extract?(path)
+      path.magic_number.match?(/\A7z\xBC\xAF\x27\x1C/n)
     end
 
     def dependencies
diff --git a/Library/Homebrew/unpack_strategy/pkg.rb b/Library/Homebrew/unpack_strategy/pkg.rb
index dceee1ef56..f837d4933c 100644
--- a/Library/Homebrew/unpack_strategy/pkg.rb
+++ b/Library/Homebrew/unpack_strategy/pkg.rb
@@ -2,9 +2,15 @@ require_relative "uncompressed"
 
 module UnpackStrategy
   class Pkg < Uncompressed
-    def self.can_extract?(path:, magic_number:)
+    using Magic
+
+    def self.extensions
+      [".pkg", ".mkpg"]
+    end
+
+    def self.can_extract?(path)
       path.extname.match?(/\A.m?pkg\Z/) &&
-        (path.directory? || magic_number.match?(/\Axar!/n))
+        (path.directory? || path.magic_number.match?(/\Axar!/n))
     end
   end
 end
diff --git a/Library/Homebrew/unpack_strategy/rar.rb b/Library/Homebrew/unpack_strategy/rar.rb
index d7ecbbf64a..648c79e972 100644
--- a/Library/Homebrew/unpack_strategy/rar.rb
+++ b/Library/Homebrew/unpack_strategy/rar.rb
@@ -2,8 +2,14 @@ module UnpackStrategy
   class Rar
     include UnpackStrategy
 
-    def self.can_extract?(path:, magic_number:)
-      magic_number.match?(/\ARar!/n)
+    using Magic
+
+    def self.extensions
+      [".rar"]
+    end
+
+    def self.can_extract?(path)
+      path.magic_number.match?(/\ARar!/n)
     end
 
     def dependencies
diff --git a/Library/Homebrew/unpack_strategy/self_extracting_executable.rb b/Library/Homebrew/unpack_strategy/self_extracting_executable.rb
index a7de316716..a502cce547 100644
--- a/Library/Homebrew/unpack_strategy/self_extracting_executable.rb
+++ b/Library/Homebrew/unpack_strategy/self_extracting_executable.rb
@@ -2,12 +2,15 @@ require_relative "generic_unar"
 
 module UnpackStrategy
   class SelfExtractingExecutable < GenericUnar
-    def self.can_extract?(path:, magic_number:)
-      return false unless magic_number.match?(/\AMZ/n)
+    using Magic
 
-      system_command("file",
-                     args: [path],
-                     print_stderr: false).stdout.include?("self-extracting")
+    def self.extensions
+      []
+    end
+
+    def self.can_extract?(path)
+      path.magic_number.match?(/\AMZ/n) &&
+        path.file_type.include?("self-extracting archive")
     end
   end
 end
diff --git a/Library/Homebrew/unpack_strategy/sit.rb b/Library/Homebrew/unpack_strategy/sit.rb
index 48098bb8cb..c719de4a04 100644
--- a/Library/Homebrew/unpack_strategy/sit.rb
+++ b/Library/Homebrew/unpack_strategy/sit.rb
@@ -2,8 +2,14 @@ require_relative "generic_unar"
 
 module UnpackStrategy
   class Sit < GenericUnar
-    def self.can_extract?(path:, magic_number:)
-      magic_number.match?(/\AStuffIt/n)
+    using Magic
+
+    def self.extensions
+      [".sit"]
+    end
+
+    def self.can_extract?(path)
+      path.magic_number.match?(/\AStuffIt/n)
     end
   end
 end
diff --git a/Library/Homebrew/unpack_strategy/subversion.rb b/Library/Homebrew/unpack_strategy/subversion.rb
index 064baf921a..3824dce378 100644
--- a/Library/Homebrew/unpack_strategy/subversion.rb
+++ b/Library/Homebrew/unpack_strategy/subversion.rb
@@ -2,7 +2,9 @@ require_relative "directory"
 
 module UnpackStrategy
   class Subversion < Directory
-    def self.can_extract?(path:, magic_number:)
+    using Magic
+
+    def self.can_extract?(path)
       super && (path/".svn").directory?
     end
 
diff --git a/Library/Homebrew/unpack_strategy/tar.rb b/Library/Homebrew/unpack_strategy/tar.rb
index 704e3890f4..a21682050d 100644
--- a/Library/Homebrew/unpack_strategy/tar.rb
+++ b/Library/Homebrew/unpack_strategy/tar.rb
@@ -2,8 +2,24 @@ module UnpackStrategy
   class Tar
     include UnpackStrategy
 
-    def self.can_extract?(path:, magic_number:)
-      return true if magic_number.match?(/\A.{257}ustar/n)
+    using Magic
+
+    def self.extensions
+      [
+        ".tar",
+        ".tbz", ".tbz2", ".tar.bz2",
+        ".tgz", ".tar.gz",
+        ".tlz", ".tar.lz",
+        ".txz", ".tar.xz"
+      ]
+    end
+
+    def self.can_extract?(path)
+      return true if path.magic_number.match?(/\A.{257}ustar/n)
+
+      unless [Bzip2, Gzip, Lzip, Xz].any? { |s| s.can_extract?(path) }
+        return false
+      end
 
       # Check if `tar` can list the contents, then it can also extract it.
       IO.popen(["tar", "tf", path], err: File::NULL) do |stdout|
@@ -14,7 +30,17 @@ module UnpackStrategy
     private
 
     def extract_to_dir(unpack_dir, basename:, verbose:)
-      system_command! "tar", args: ["xf", path, "-C", unpack_dir]
+      Dir.mktmpdir do |tmpdir|
+        tar_path = path
+
+        if DependencyCollector.tar_needs_xz_dependency? && Xz.can_extract?(path)
+          tmpdir = Pathname(tmpdir)
+          Xz.new(path).extract(to: tmpdir)
+          tar_path = tmpdir.children.first
+        end
+
+        system_command! "tar", args: ["xf", tar_path, "-C", unpack_dir]
+      end
     end
   end
 end
diff --git a/Library/Homebrew/unpack_strategy/ttf.rb b/Library/Homebrew/unpack_strategy/ttf.rb
index 8d1421a106..e5f0540c0b 100644
--- a/Library/Homebrew/unpack_strategy/ttf.rb
+++ b/Library/Homebrew/unpack_strategy/ttf.rb
@@ -2,11 +2,17 @@ require_relative "uncompressed"
 
 module UnpackStrategy
   class Ttf < Uncompressed
-    def self.can_extract?(path:, magic_number:)
+    using Magic
+
+    def self.extensions
+      [".ttc", ".ttf"]
+    end
+
+    def self.can_extract?(path)
       # TrueType Font
-      magic_number.match?(/\A\000\001\000\000\000/n) ||
+      path.magic_number.match?(/\A\000\001\000\000\000/n) ||
         # Truetype Font Collection
-        magic_number.match?(/\Attcf/n)
+        path.magic_number.match?(/\Attcf/n)
     end
   end
 end
diff --git a/Library/Homebrew/unpack_strategy/uncompressed.rb b/Library/Homebrew/unpack_strategy/uncompressed.rb
index b3facb172c..fe627bf818 100644
--- a/Library/Homebrew/unpack_strategy/uncompressed.rb
+++ b/Library/Homebrew/unpack_strategy/uncompressed.rb
@@ -2,7 +2,9 @@ module UnpackStrategy
   class Uncompressed
     include UnpackStrategy
 
-    alias extract_nestedly extract
+    def extract_nestedly(extension_only: false, **options)
+      extract(**options)
+    end
 
     private
 
diff --git a/Library/Homebrew/unpack_strategy/xar.rb b/Library/Homebrew/unpack_strategy/xar.rb
index b631aba77d..043c6a5f49 100644
--- a/Library/Homebrew/unpack_strategy/xar.rb
+++ b/Library/Homebrew/unpack_strategy/xar.rb
@@ -2,8 +2,14 @@ module UnpackStrategy
   class Xar
     include UnpackStrategy
 
-    def self.can_extract?(path:, magic_number:)
-      magic_number.match?(/\Axar!/n)
+    using Magic
+
+    def self.extensions
+      [".xar"]
+    end
+
+    def self.can_extract?(path)
+      path.magic_number.match?(/\Axar!/n)
     end
 
     private
diff --git a/Library/Homebrew/unpack_strategy/xz.rb b/Library/Homebrew/unpack_strategy/xz.rb
index c7f418cede..99673e6159 100644
--- a/Library/Homebrew/unpack_strategy/xz.rb
+++ b/Library/Homebrew/unpack_strategy/xz.rb
@@ -2,8 +2,14 @@ module UnpackStrategy
   class Xz
     include UnpackStrategy
 
-    def self.can_extract?(path:, magic_number:)
-      magic_number.match?(/\A\xFD7zXZ\x00/n)
+    using Magic
+
+    def self.extensions
+      [".xz"]
+    end
+
+    def self.can_extract?(path)
+      path.magic_number.match?(/\A\xFD7zXZ\x00/n)
     end
 
     def dependencies
@@ -18,19 +24,6 @@ module UnpackStrategy
       system_command! "unxz",
                       args: [*quiet_flags, "-T0", "--", unpack_dir/basename],
                       env: { "PATH" => PATH.new(Formula["xz"].opt_bin, ENV["PATH"]) }
-      extract_nested_tar(unpack_dir)
-    end
-
-    def extract_nested_tar(unpack_dir)
-      return unless DependencyCollector.tar_needs_xz_dependency?
-      return if (children = unpack_dir.children).count != 1
-      return if (tar = children.first).extname != ".tar"
-
-      Dir.mktmpdir do |tmpdir|
-        tmpdir = Pathname(tmpdir)
-        FileUtils.mv tar, tmpdir/tar.basename
-        Tar.new(tmpdir/tar.basename).extract(to: unpack_dir)
-      end
     end
   end
 end
diff --git a/Library/Homebrew/unpack_strategy/zip.rb b/Library/Homebrew/unpack_strategy/zip.rb
index df3a0c1220..d8188447ba 100644
--- a/Library/Homebrew/unpack_strategy/zip.rb
+++ b/Library/Homebrew/unpack_strategy/zip.rb
@@ -2,8 +2,14 @@ module UnpackStrategy
   class Zip
     include UnpackStrategy
 
-    def self.can_extract?(path:, magic_number:)
-      magic_number.match?(/\APK(\003\004|\005\006)/n)
+    using Magic
+
+    def self.extensions
+      [".zip"]
+    end
+
+    def self.can_extract?(path)
+      path.magic_number.match?(/\APK(\003\004|\005\006)/n)
     end
 
     private