diff --git a/Library/Homebrew/cmd/upgrade.rb b/Library/Homebrew/cmd/upgrade.rb
index e1488c2fd7..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)
+  def broken_dependents(kegs, formulae, scanned = Set.new)
     formulae_to_reinstall = Set.new
     formulae_pinned_and_outdated = Set.new
 
@@ -264,8 +264,9 @@ module Homebrew
         descendants = Set.new
 
         dependents = kegs.select do |keg|
-          keg.runtime_dependencies
-             .any? { |d| d["full_name"] == formula.full_name }
+          keg = keg.runtime_dependencies
+                   .any? { |d| d["full_name"] == formula.full_name }
+          keg unless scanned.include?(keg)
         end
 
         next if dependents.empty?
@@ -290,7 +291,9 @@ module Homebrew
           descendants << f
         end
 
-        descendants_to_reinstall, descendants_pinned = broken_dependents(kegs, descendants)
+        scanned.merge dependents
+
+        descendants_to_reinstall, descendants_pinned = broken_dependents(kegs, descendants, scanned)
 
         formulae_to_reinstall.merge descendants_to_reinstall
         formulae_pinned_and_outdated.merge descendants_pinned