diff --git a/Library/Homebrew/cmd/upgrade.rb b/Library/Homebrew/cmd/upgrade.rb
index 1797f872cb..781f425425 100644
--- a/Library/Homebrew/cmd/upgrade.rb
+++ b/Library/Homebrew/cmd/upgrade.rb
@@ -255,7 +255,7 @@ module Homebrew
     [formulae_to_upgrade, formulae_pinned]
   end
 
-  def broken_dependents(kegs, formulae, scanned = [])
+  def broken_dependents(kegs, formulae, scanned = Set.new)
     formulae_to_reinstall = Set.new
     formulae_pinned_and_outdated = Set.new
 
@@ -264,10 +264,9 @@ module Homebrew
         descendants = Set.new
 
         dependents = kegs.select do |keg|
-          keg.runtime_dependencies
-             .any? { |d| d["full_name"] == formula.full_name }
-        end.reject do |keg|
-          scanned.include?(keg)
+          keg = keg.runtime_dependencies
+                   .any? { |d| d["full_name"] == formula.full_name }
+          keg unless scanned.include?(keg)
         end
 
         next if dependents.empty?
@@ -292,7 +291,7 @@ module Homebrew
           descendants << f
         end
 
-        scanned << dependents
+        scanned.merge dependents
 
         descendants_to_reinstall, descendants_pinned = broken_dependents(kegs, descendants, scanned)