diff --git a/doc/stdenv/stdenv.chapter.md b/doc/stdenv/stdenv.chapter.md
index 5f7f45dc443..958747d3404 100644
--- a/doc/stdenv/stdenv.chapter.md
+++ b/doc/stdenv/stdenv.chapter.md
@@ -731,6 +731,10 @@ If set, files in `$out/sbin` are not moved to `$out/bin`. By default, they are.
 
 List of directories to search for libraries and executables from which *all* symbols should be stripped. By default, it’s empty. Stripping all symbols is risky, since it may remove not just debug symbols but also ELF information necessary for normal execution.
 
+##### `stripAllListTarget` {#var-stdenv-stripAllListTarget}
+
+Like `stripAllList`, but only applies to packages’ target platform. By default, it’s empty. Useful when supporting cross compilation.
+
 ##### `stripAllFlags` {#var-stdenv-stripAllFlags}
 
 Flags passed to the `strip` command applied to the files in the directories listed in `stripAllList`. Defaults to `-s` (i.e. `--strip-all`).
@@ -739,6 +743,10 @@ Flags passed to the `strip` command applied to the files in the directories list
 
 List of directories to search for libraries and executables from which only debugging-related symbols should be stripped. It defaults to `lib lib32 lib64 libexec bin sbin`.
 
+##### `stripDebugListTarget` {#var-stdenv-stripDebugListTarget}
+
+Like `stripDebugList`, but only applies to packages’ target platform. By default, it’s empty. Useful when supporting cross compilation.
+
 ##### `stripDebugFlags` {#var-stdenv-stripDebugFlags}
 
 Flags passed to the `strip` command applied to the files in the directories listed in `stripDebugList`. Defaults to `-S` (i.e. `--strip-debug`).
diff --git a/pkgs/build-support/setup-hooks/strip.sh b/pkgs/build-support/setup-hooks/strip.sh
index a23b203aff5..9d0b163f4c4 100644
--- a/pkgs/build-support/setup-hooks/strip.sh
+++ b/pkgs/build-support/setup-hooks/strip.sh
@@ -7,31 +7,29 @@ _doStrip() {
     # to $out anyways---if it does, that's a bigger problem that a lack of
     # stripping will help catch.
     local -ra flags=(dontStripHost dontStripTarget)
+    local -ra debugDirs=(stripDebugList stripDebugListTarget)
+    local -ra allDirs=(stripAllList stripAllListTarget)
     local -ra stripCmds=(STRIP STRIP_FOR_TARGET)
 
-    # Optimization
-    if [[ "${STRIP-}" == "${STRIP_FOR_TARGET-}" ]]; then
-        dontStripTarget+=1
-    fi
+    # Strip only host paths by default. Leave targets as is.
+    stripDebugList=${stripDebugList:-lib lib32 lib64 libexec bin sbin}
+    stripDebugListTarget=${stripDebugListTarget:-}
+    stripAllList=${stripAllList:-}
+    stripAllListTarget=${stripAllListTarget:-}
 
     local i
     for i in ${!stripCmds[@]}; do
         local -n flag="${flags[$i]}"
+        local -n debugDirList="${debugDirs[$i]}"
+        local -n allDirList="${allDirs[$i]}"
         local -n stripCmd="${stripCmds[$i]}"
 
         # `dontStrip` disables them all
         if [[ "${dontStrip-}" || "${flag-}" ]] || ! type -f "${stripCmd-}" 2>/dev/null
         then continue; fi
 
-        stripDebugList=${stripDebugList:-lib lib32 lib64 libexec bin sbin}
-        if [ -n "$stripDebugList" ]; then
-            stripDirs "$stripCmd" "$stripDebugList" "${stripDebugFlags:--S}"
-        fi
-
-        stripAllList=${stripAllList:-}
-        if [ -n "$stripAllList" ]; then
-            stripDirs "$stripCmd" "$stripAllList" "${stripAllFlags:--s}"
-        fi
+        stripDirs "$stripCmd" "$debugDirList" "${stripDebugFlags:--S}"
+        stripDirs "$stripCmd" "$allDirList" "${stripAllFlags:--s}"
     done
 }
 
@@ -50,8 +48,7 @@ stripDirs() {
     dirs=${dirsNew}
 
     if [ -n "${dirs}" ]; then
-        header "stripping (with command $cmd and flags $stripFlags) in$dirs"
+        echo "stripping (with command $cmd and flags $stripFlags) in$dirs"
         find $dirs -type f -exec $cmd $stripFlags '{}' \; 2>/dev/null
-        stopNest
     fi
 }