diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index ae1ed55..4c44ac9 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -57,8 +57,16 @@ jobs:
             os: ubuntu-20.04
             target: i586-unknown-linux-musl
             expect_file_re: "ELF.+80386"
-            expect_cross: "--no-expect-cross"
-            expect_stripped: "--expect-stripped"
+            expect_cross: "--expect-cross"
+            expect_stripped: "--no-expect-stripped"
+            can_test: true
+
+          - platform_name: Linux-i686
+            os: ubuntu-20.04
+            target: i686-unknown-linux-musl
+            expect_file_re: "ELF.+80386"
+            expect_cross: "--expect-cross"
+            expect_stripped: "--no-expect-stripped"
             can_test: true
 
           - platform_name: Linux-mips
diff --git a/Changes.md b/Changes.md
index 1e9c877..63c3eef 100644
--- a/Changes.md
+++ b/Changes.md
@@ -1,3 +1,7 @@
+- Use `cross` when compiling for 32-bit Linux targets. While in theory this should work without
+  `cross`, compiling `openssl` with the `vendored` feature fails when we run
+  `cargo build --target i686-unknown-linux-musl`.
+
 ## 0.0.10 - 2023-12-10
 
 - Fixed handling of crates with multiple binaries. Attempting to strip binaries for such a crate
diff --git a/set-cross-compile.sh b/set-cross-compile.sh
index 29f7ce3..a8119b6 100755
--- a/set-cross-compile.sh
+++ b/set-cross-compile.sh
@@ -10,7 +10,11 @@ if uname -a | grep --quiet --extended-regexp -i "darwin|msys|windows"; then
     exit 0
 fi
 
-if echo "$TARGET" | grep --quiet --extended-regexp -i '(x86_64|586|686).+linux-(gnu|musl)'; then
+# On Linux, we should be able to cross-compile to i586 and i686, but in
+# practice this fails with some crates, notably openssl with the "vendored"
+# feature. This feature makes it compile openssl itself, which fails without
+# cross.
+if echo "$TARGET" | grep --quiet --extended-regexp -i 'x86_64.+linux-(gnu|musl)'; then
     echo "needs-cross=false" >> $GITHUB_OUTPUT
     exit 0
 fi