diff --git a/gnu/packages/cross-base.scm b/gnu/packages/cross-base.scm
index ca8d432d96..28224a1c40 100644
--- a/gnu/packages/cross-base.scm
+++ b/gnu/packages/cross-base.scm
@@ -251,9 +251,6 @@ XBINUTILS and the cross tool chain."
               #t))
           ,phases))))
 
-    ;; Remove the "debug" output since stripping is disabled.
-    (outputs (delete "debug" (package-outputs glibc)))
-
     (propagated-inputs `(("cross-linux-headers" ,xlinux-headers)))
     (native-inputs `(("cross-gcc" ,xgcc)
                      ("cross-binutils" ,xbinutils)
diff --git a/guix/build-system/gnu.scm b/guix/build-system/gnu.scm
index d074294b4c..c12a871fd8 100644
--- a/guix/build-system/gnu.scm
+++ b/guix/build-system/gnu.scm
@@ -299,7 +299,9 @@ which could lead to gratuitous input divergence."
                                   ,@(if implicit-inputs?
                                         implicit-inputs
                                         '()))
-                                #:outputs outputs
+                                #:outputs (if strip-binaries?
+                                              outputs
+                                              (delete "debug" outputs))
                                 #:modules imported-modules
                                 #:guile-for-build guile-for-build))
 
@@ -470,7 +472,9 @@ platform."
                                   ,@(if implicit-inputs?
                                         implicit-host-inputs
                                         '()))
-                                #:outputs outputs
+                                #:outputs (if strip-binaries?
+                                              outputs
+                                              (delete "debug" outputs))
                                 #:modules imported-modules
                                 #:guile-for-build guile-for-build))