diff --git a/Library/Homebrew/unpack_strategy.rb b/Library/Homebrew/unpack_strategy.rb
index e0ed8caca9..3a06993f4b 100644
--- a/Library/Homebrew/unpack_strategy.rb
+++ b/Library/Homebrew/unpack_strategy.rb
@@ -43,17 +43,17 @@ module UnpackStrategy
       Xar,
       Ttf,
       Otf,
-      Executable,
       Git,
       Mercurial,
       Subversion,
       Cvs,
+      SelfExtractingExecutable, # needs to be before Cab
+      Cab,
+      Executable,
       Dmg, # needs to be before Bzip2
       Bzip2,
       Fossil,
       Bazaar,
-      SelfExtractingExecutable, # needs to be before Cab
-      Cab,
       Compress,
       P7Zip,
       Sit,
@@ -77,19 +77,14 @@ module UnpackStrategy
   end
 
   def self.from_path(path)
-    strategy = strategies.detect do |s|
-      s.can_extract?(path)
-    end
+    strategy = strategies
+               .sort_by { |s| s.extensions.map(&:length).max(0) }
+               .reverse
+               .detect { |s| s.extensions.include?(path.extname) }
 
-    # 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 ||= strategies.detect { |s| s.can_extract?(path) }
+
+    strategy ||= Uncompressed
 
     strategy
   end
diff --git a/Library/Homebrew/unpack_strategy/air.rb b/Library/Homebrew/unpack_strategy/air.rb
index eabcefbacf..1b12e221b0 100644
--- a/Library/Homebrew/unpack_strategy/air.rb
+++ b/Library/Homebrew/unpack_strategy/air.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
 
     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)}/)
diff --git a/Library/Homebrew/unpack_strategy/bzip2.rb b/Library/Homebrew/unpack_strategy/bzip2.rb
index aa56ab711a..e47cc062df 100644
--- a/Library/Homebrew/unpack_strategy/bzip2.rb
+++ b/Library/Homebrew/unpack_strategy/bzip2.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
 
     using Magic
 
+    def self.extensions
+      [".bz2"]
+    end
+
     def self.can_extract?(path)
       path.magic_number.match?(/\ABZh/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/cab.rb b/Library/Homebrew/unpack_strategy/cab.rb
index 346ac014f2..afbf9e3784 100644
--- a/Library/Homebrew/unpack_strategy/cab.rb
+++ b/Library/Homebrew/unpack_strategy/cab.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
 
     using Magic
 
+    def self.extensions
+      [".cab"]
+    end
+
     def self.can_extract?(path)
       path.magic_number.match?(/\AMSCF/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/compress.rb b/Library/Homebrew/unpack_strategy/compress.rb
index be7039beb6..952e17c980 100644
--- a/Library/Homebrew/unpack_strategy/compress.rb
+++ b/Library/Homebrew/unpack_strategy/compress.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
   class Compress < Tar
     using Magic
 
+    def self.extensions
+      [".compress"]
+    end
+
     def self.can_extract?(path)
       path.magic_number.match?(/\A\037\235/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/directory.rb b/Library/Homebrew/unpack_strategy/directory.rb
index b8909bc0ef..5aa39e9137 100644
--- a/Library/Homebrew/unpack_strategy/directory.rb
+++ b/Library/Homebrew/unpack_strategy/directory.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
 
     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 e2f3b83322..b15ec3c44d 100644
--- a/Library/Homebrew/unpack_strategy/dmg.rb
+++ b/Library/Homebrew/unpack_strategy/dmg.rb
@@ -92,14 +92,11 @@ module UnpackStrategy
     end
     private_constant :Mount
 
+    def self.extensions
+      [".dmg"]
+    end
+
     def self.can_extract?(path)
-      bzip2 = Bzip2.can_extract?(path)
-
-      zlib = path.magic_number.match?(/\A(\x78|\x08|\x18|\x28|\x38|\x48|\x58|\x68)/n) &&
-             (path.magic_number[0...2].unpack("S>").first % 31).zero?
-
-      return false unless bzip2 || zlib
-
       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 b7b2d9cb9a..3378bb6ff1 100644
--- a/Library/Homebrew/unpack_strategy/executable.rb
+++ b/Library/Homebrew/unpack_strategy/executable.rb
@@ -4,8 +4,13 @@ module UnpackStrategy
   class Executable < Uncompressed
     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?(/\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 9effd39874..5bc5e5e78f 100644
--- a/Library/Homebrew/unpack_strategy/fossil.rb
+++ b/Library/Homebrew/unpack_strategy/fossil.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
 
     using Magic
 
+    def self.extensions
+      []
+    end
+
     def self.can_extract?(path)
       return false unless path.magic_number.match?(/\ASQLite format 3\000/n)
 
diff --git a/Library/Homebrew/unpack_strategy/generic_unar.rb b/Library/Homebrew/unpack_strategy/generic_unar.rb
index 228e8fd05d..f9e65b9dec 100644
--- a/Library/Homebrew/unpack_strategy/generic_unar.rb
+++ b/Library/Homebrew/unpack_strategy/generic_unar.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
 
     using Magic
 
+    def self.extensions
+      []
+    end
+
     def self.can_extract?(_path)
       false
     end
diff --git a/Library/Homebrew/unpack_strategy/gzip.rb b/Library/Homebrew/unpack_strategy/gzip.rb
index c9dcc48d06..d575721d74 100644
--- a/Library/Homebrew/unpack_strategy/gzip.rb
+++ b/Library/Homebrew/unpack_strategy/gzip.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
 
     using Magic
 
+    def self.extensions
+      [".gz"]
+    end
+
     def self.can_extract?(path)
       path.magic_number.match?(/\A\037\213/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/jar.rb b/Library/Homebrew/unpack_strategy/jar.rb
index 6c23d29f1f..90d4f6485c 100644
--- a/Library/Homebrew/unpack_strategy/jar.rb
+++ b/Library/Homebrew/unpack_strategy/jar.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
   class Jar < Uncompressed
     using Magic
 
+    def self.extensions
+      [".apk", ".jar"]
+    end
+
     def self.can_extract?(path)
       return false unless Zip.can_extract?(path)
 
diff --git a/Library/Homebrew/unpack_strategy/lha.rb b/Library/Homebrew/unpack_strategy/lha.rb
index c0ade6f5e1..b3671b0a60 100644
--- a/Library/Homebrew/unpack_strategy/lha.rb
+++ b/Library/Homebrew/unpack_strategy/lha.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
 
     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
diff --git a/Library/Homebrew/unpack_strategy/lua_rock.rb b/Library/Homebrew/unpack_strategy/lua_rock.rb
index e6bf7bf336..fe3d8f130b 100644
--- a/Library/Homebrew/unpack_strategy/lua_rock.rb
+++ b/Library/Homebrew/unpack_strategy/lua_rock.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
   class LuaRock < Uncompressed
     using Magic
 
+    def self.extensions
+      [".rock"]
+    end
+
     def self.can_extract?(path)
       return false unless Zip.can_extract?(path)
 
diff --git a/Library/Homebrew/unpack_strategy/lzip.rb b/Library/Homebrew/unpack_strategy/lzip.rb
index 364dd2139f..f96e0ab2da 100644
--- a/Library/Homebrew/unpack_strategy/lzip.rb
+++ b/Library/Homebrew/unpack_strategy/lzip.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
 
     using Magic
 
+    def self.extensions
+      [".lz"]
+    end
+
     def self.can_extract?(path)
       path.magic_number.match?(/\ALZIP/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/lzma.rb b/Library/Homebrew/unpack_strategy/lzma.rb
index 189495c37f..a9a60a0b9a 100644
--- a/Library/Homebrew/unpack_strategy/lzma.rb
+++ b/Library/Homebrew/unpack_strategy/lzma.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
 
     using Magic
 
+    def self.extensions
+      [".lzma"]
+    end
+
     def self.can_extract?(path)
       path.magic_number.match?(/\A\]\000\000\200\000/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/microsoft_office_xml.rb b/Library/Homebrew/unpack_strategy/microsoft_office_xml.rb
index 7d40000773..50647869e2 100644
--- a/Library/Homebrew/unpack_strategy/microsoft_office_xml.rb
+++ b/Library/Homebrew/unpack_strategy/microsoft_office_xml.rb
@@ -4,6 +4,14 @@ module UnpackStrategy
   class MicrosoftOfficeXml < Uncompressed
     using Magic
 
+    def self.extensions
+      [
+        ".doc", ".docx",
+        ".ppt", ".pptx",
+        ".xls", ".xlsx"
+      ]
+    end
+
     def self.can_extract?(path)
       return false unless Zip.can_extract?(path)
 
diff --git a/Library/Homebrew/unpack_strategy/otf.rb b/Library/Homebrew/unpack_strategy/otf.rb
index 87d7c860d5..a540f7779f 100644
--- a/Library/Homebrew/unpack_strategy/otf.rb
+++ b/Library/Homebrew/unpack_strategy/otf.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
   class Otf < Uncompressed
     using Magic
 
+    def self.extensions
+      [".otf"]
+    end
+
     def self.can_extract?(path)
       path.magic_number.match?(/\AOTTO/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/p7zip.rb b/Library/Homebrew/unpack_strategy/p7zip.rb
index fa4fd3b7f1..cfb76d08c9 100644
--- a/Library/Homebrew/unpack_strategy/p7zip.rb
+++ b/Library/Homebrew/unpack_strategy/p7zip.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
 
     using Magic
 
+    def self.extensions
+      [".7z"]
+    end
+
     def self.can_extract?(path)
       path.magic_number.match?(/\A7z\xBC\xAF\x27\x1C/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/pkg.rb b/Library/Homebrew/unpack_strategy/pkg.rb
index a9f6597972..f837d4933c 100644
--- a/Library/Homebrew/unpack_strategy/pkg.rb
+++ b/Library/Homebrew/unpack_strategy/pkg.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
   class Pkg < Uncompressed
     using Magic
 
+    def self.extensions
+      [".pkg", ".mkpg"]
+    end
+
     def self.can_extract?(path)
       path.extname.match?(/\A.m?pkg\Z/) &&
         (path.directory? || path.magic_number.match?(/\Axar!/n))
diff --git a/Library/Homebrew/unpack_strategy/rar.rb b/Library/Homebrew/unpack_strategy/rar.rb
index 4b3d6acba6..648c79e972 100644
--- a/Library/Homebrew/unpack_strategy/rar.rb
+++ b/Library/Homebrew/unpack_strategy/rar.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
 
     using Magic
 
+    def self.extensions
+      [".rar"]
+    end
+
     def self.can_extract?(path)
       path.magic_number.match?(/\ARar!/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/self_extracting_executable.rb b/Library/Homebrew/unpack_strategy/self_extracting_executable.rb
index 9c442d778d..a502cce547 100644
--- a/Library/Homebrew/unpack_strategy/self_extracting_executable.rb
+++ b/Library/Homebrew/unpack_strategy/self_extracting_executable.rb
@@ -4,10 +4,13 @@ module UnpackStrategy
   class SelfExtractingExecutable < GenericUnar
     using Magic
 
-    def self.can_extract?(path)
-      return false unless path.magic_number.match?(/\AMZ/n)
+    def self.extensions
+      []
+    end
 
-      path.file_type.include?("self-extracting archive")
+    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 57ada1253c..c719de4a04 100644
--- a/Library/Homebrew/unpack_strategy/sit.rb
+++ b/Library/Homebrew/unpack_strategy/sit.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
   class Sit < GenericUnar
     using Magic
 
+    def self.extensions
+      [".sit"]
+    end
+
     def self.can_extract?(path)
       path.magic_number.match?(/\AStuffIt/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/tar.rb b/Library/Homebrew/unpack_strategy/tar.rb
index b19f127764..fcd67a3d49 100644
--- a/Library/Homebrew/unpack_strategy/tar.rb
+++ b/Library/Homebrew/unpack_strategy/tar.rb
@@ -4,6 +4,16 @@ module UnpackStrategy
 
     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)
 
diff --git a/Library/Homebrew/unpack_strategy/ttf.rb b/Library/Homebrew/unpack_strategy/ttf.rb
index 664f6f766e..e5f0540c0b 100644
--- a/Library/Homebrew/unpack_strategy/ttf.rb
+++ b/Library/Homebrew/unpack_strategy/ttf.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
   class Ttf < Uncompressed
     using Magic
 
+    def self.extensions
+      [".ttc", ".ttf"]
+    end
+
     def self.can_extract?(path)
       # TrueType Font
       path.magic_number.match?(/\A\000\001\000\000\000/n) ||
diff --git a/Library/Homebrew/unpack_strategy/xar.rb b/Library/Homebrew/unpack_strategy/xar.rb
index 903732dc31..043c6a5f49 100644
--- a/Library/Homebrew/unpack_strategy/xar.rb
+++ b/Library/Homebrew/unpack_strategy/xar.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
 
     using Magic
 
+    def self.extensions
+      [".xar"]
+    end
+
     def self.can_extract?(path)
       path.magic_number.match?(/\Axar!/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/xz.rb b/Library/Homebrew/unpack_strategy/xz.rb
index 1cbb23b330..c53d2681d5 100644
--- a/Library/Homebrew/unpack_strategy/xz.rb
+++ b/Library/Homebrew/unpack_strategy/xz.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
 
     using Magic
 
+    def self.extensions
+      [".xz"]
+    end
+
     def self.can_extract?(path)
       path.magic_number.match?(/\A\xFD7zXZ\x00/n)
     end
diff --git a/Library/Homebrew/unpack_strategy/zip.rb b/Library/Homebrew/unpack_strategy/zip.rb
index 237d43f3f5..d8188447ba 100644
--- a/Library/Homebrew/unpack_strategy/zip.rb
+++ b/Library/Homebrew/unpack_strategy/zip.rb
@@ -4,6 +4,10 @@ module UnpackStrategy
 
     using Magic
 
+    def self.extensions
+      [".zip"]
+    end
+
     def self.can_extract?(path)
       path.magic_number.match?(/\APK(\003\004|\005\006)/n)
     end