diff --git a/Library/Homebrew/cask/cask.rb b/Library/Homebrew/cask/cask.rb
index 9775e80bd8..915beb71b9 100644
--- a/Library/Homebrew/cask/cask.rb
+++ b/Library/Homebrew/cask/cask.rb
@@ -38,6 +38,16 @@ module Cask
       end.compact
     end
 
+    def self.full_names
+      Tap.flat_map do |tap|
+        next tap.cask_tokens.blank?
+        next tap.cask_tokens if tap.user == "Homebrew"
+
+        name = tap.name
+        tap.cask_tokens.map { |tok| "#{name}/#{tok}" }
+      end.flatten
+    end
+
     def tap
       return super if block_given? # Object#tap
 
diff --git a/Library/Homebrew/extend/os/mac/search.rb b/Library/Homebrew/extend/os/mac/search.rb
index cbe7a8adff..6a094d30bd 100644
--- a/Library/Homebrew/extend/os/mac/search.rb
+++ b/Library/Homebrew/extend/os/mac/search.rb
@@ -37,7 +37,7 @@ module Homebrew
         results = cask_tokens.extend(Searchable)
                              .search(string_or_regex)
 
-        cask_names = Cask::Cask.all.map(&:full_name)
+        cask_names = Cask::Cask.full_names
         results += DidYouMean::SpellChecker.new(dictionary: cask_names)
                                            .correct(string_or_regex)