diff --git a/Library/Homebrew/formula_installer.rb b/Library/Homebrew/formula_installer.rb
index 0cc5470bcb..e070a466c3 100644
--- a/Library/Homebrew/formula_installer.rb
+++ b/Library/Homebrew/formula_installer.rb
@@ -598,16 +598,16 @@ class FormulaInstaller
     oh1 "Installing #{formula.full_name} dependency: #{Formatter.identifier(dep.name)}"
     fi.install
     fi.finish
-  rescue FormulaInstallationAlreadyAttemptedError
-    # We already attempted to install f as part of the dependency tree of
-    # another formula. In that case, don't generate an error, just move on.
-    nil
-  rescue Exception # rubocop:disable Lint/RescueException
+  rescue Exception => e # rubocop:disable Lint/RescueException
     ignore_interrupts do
       tmp_keg.rename(installed_keg) if tmp_keg && !installed_keg.directory?
       linked_keg.link if keg_was_linked
     end
-    raise
+    raise unless e.is_a? FormulaInstallationAlreadyAttemptedError
+
+    # We already attempted to install f as part of another formula's
+    # dependency tree. In that case, don't generate an error, just move on.
+    nil
   else
     ignore_interrupts { tmp_keg.rmtree if tmp_keg&.directory? }
   end