diff --git a/src/bootstrap/builder.rs b/src/bootstrap/builder.rs
index a24a6a4636d48..c62548875bf98 100644
--- a/src/bootstrap/builder.rs
+++ b/src/bootstrap/builder.rs
@@ -302,8 +302,10 @@ impl StepDescription {
         }
     }
 
-    fn maybe_run(&self, builder: &Builder<'_>, pathsets: Vec<PathSet>) {
-        if pathsets.iter().any(|set| self.is_excluded(builder, set)) {
+    fn maybe_run(&self, builder: &Builder<'_>, mut pathsets: Vec<PathSet>) {
+        pathsets.retain(|set| !self.is_excluded(builder, set));
+
+        if pathsets.is_empty() {
             return;
         }
 
diff --git a/src/bootstrap/builder/tests.rs b/src/bootstrap/builder/tests.rs
index 43b4a34fe5b62..80e66622e8b92 100644
--- a/src/bootstrap/builder/tests.rs
+++ b/src/bootstrap/builder/tests.rs
@@ -136,9 +136,9 @@ fn test_exclude_kind() {
     let mut config = configure("test", &["A"], &["A"]);
     // Ensure our test is valid, and `test::Rustc` would be run without the exclude.
     assert!(run_build(&[], config.clone()).contains::<test::CrateLibrustc>());
-    // Ensure tests for rustc are skipped.
+    // Ensure tests for rustc are not skipped.
     config.skip = vec![path.clone()];
-    assert!(!run_build(&[], config.clone()).contains::<test::CrateLibrustc>());
+    assert!(run_build(&[], config.clone()).contains::<test::CrateLibrustc>());
     // Ensure builds for rustc are not skipped.
     assert!(run_build(&[], config).contains::<compile::Rustc>());
 }
diff --git a/src/ci/docker/host-x86_64/wasm32/Dockerfile b/src/ci/docker/host-x86_64/wasm32/Dockerfile
index 02b4664eb557c..0d0f1edd003cb 100644
--- a/src/ci/docker/host-x86_64/wasm32/Dockerfile
+++ b/src/ci/docker/host-x86_64/wasm32/Dockerfile
@@ -58,5 +58,6 @@ ENV NO_CHANGE_USER=1
 RUN chown 10719 -R /emsdk-portable/
 
 # Exclude library/alloc due to OOM in benches.
+# FIXME: Fix std tests
 ENV SCRIPT python3 ../x.py test --stage 2 --host='' --target $TARGETS \
-    --skip library/alloc
+    --skip library/alloc --skip library/std