diff --git a/Library/Homebrew/cmd/readall.rb b/Library/Homebrew/cmd/readall.rb
index f006838eac..339819f0d0 100644
--- a/Library/Homebrew/cmd/readall.rb
+++ b/Library/Homebrew/cmd/readall.rb
@@ -38,7 +38,6 @@ module Homebrew
     if ARGV.named.empty?
       formulae = Formula.files
       alias_dirs = Tap.map(&:alias_dir)
-      alias_dirs.unshift CoreTap.instance.alias_dir
     else
       tap = Tap.fetch(ARGV.named.first)
       raise TapUnavailableError, tap.name unless tap.installed?
diff --git a/Library/Homebrew/cmd/tap-info.rb b/Library/Homebrew/cmd/tap-info.rb
index 0a59341fff..683a2848d3 100644
--- a/Library/Homebrew/cmd/tap-info.rb
+++ b/Library/Homebrew/cmd/tap-info.rb
@@ -10,8 +10,6 @@ module Homebrew
       end
     end
 
-    raise "#{tap} is not allowed" if taps.any?(&:core_tap?)
-
     if ARGV.json == "v1"
       print_tap_json(taps)
     else
diff --git a/Library/Homebrew/formula.rb b/Library/Homebrew/formula.rb
index c2363fcde2..d9c648c9c9 100644
--- a/Library/Homebrew/formula.rb
+++ b/Library/Homebrew/formula.rb
@@ -1073,13 +1073,13 @@ class Formula
   # an array of all tap {Formula} names
   # @private
   def self.tap_names
-    @tap_names ||= Tap.flat_map(&:formula_names).sort
+    @tap_names ||= Tap.reject(&:core_tap?).flat_map(&:formula_names).sort
   end
 
   # an array of all tap {Formula} files
   # @private
   def self.tap_files
-    @tap_files ||= Tap.flat_map(&:formula_files)
+    @tap_files ||= Tap.reject(&:core_tap?).flat_map(&:formula_files)
   end
 
   # an array of all {Formula} names
@@ -1152,7 +1152,7 @@ class Formula
   # an array of all tap aliases
   # @private
   def self.tap_aliases
-    @tap_aliases ||= Tap.flat_map(&:aliases).sort
+    @tap_aliases ||= Tap.reject(&:core_tap?).flat_map(&:aliases).sort
   end
 
   # an array of all aliases
diff --git a/Library/Homebrew/formulary.rb b/Library/Homebrew/formulary.rb
index da70aed2f9..79e4c946bd 100644
--- a/Library/Homebrew/formulary.rb
+++ b/Library/Homebrew/formulary.rb
@@ -344,7 +344,7 @@ class Formulary
       if core_path(ref).file?
         opoo <<-EOS.undent
           #{ref} is provided by core, but is now shadowed by #{selected_formula.full_name}.
-          To refer to the core formula, use Homebrew/homebrew/#{ref} instead.
+          To refer to the core formula, use Homebrew/core/#{ref} instead.
         EOS
       end
       selected_formula
diff --git a/Library/Homebrew/tab.rb b/Library/Homebrew/tab.rb
index 41697abb83..9b6f284038 100644
--- a/Library/Homebrew/tab.rb
+++ b/Library/Homebrew/tab.rb
@@ -52,8 +52,9 @@ class Tab < OpenStruct
       attributes["source"]["tap"] = attributes.delete("tapped_from")
     end
 
-    if attributes["source"]["tap"] == "mxcl/master"
-      attributes["source"]["tap"] = "Homebrew/homebrew"
+    if attributes["source"]["tap"] == "mxcl/master" ||
+      attributes["source"]["tap"] == "Homebrew/homebrew"
+      attributes["source"]["tap"] = "homebrew/core"
     end
 
     if attributes["source"]["spec"].nil?
diff --git a/Library/Homebrew/tap.rb b/Library/Homebrew/tap.rb
index 32ef0fb9e1..0214b39f92 100644
--- a/Library/Homebrew/tap.rb
+++ b/Library/Homebrew/tap.rb
@@ -30,7 +30,7 @@ class Tap
     user = "Homebrew" if user == "homebrew"
     repo = repo.strip_prefix "homebrew-"
 
-    if user == "Homebrew" && repo == "homebrew"
+    if user == "Homebrew" && (repo == "homebrew" || repo == "core")
       return CoreTap.instance
     end