diff --git a/src/tools/run-make-support/src/lib.rs b/src/tools/run-make-support/src/lib.rs
index 294dae109425f..9a180fe4ad19a 100644
--- a/src/tools/run-make-support/src/lib.rs
+++ b/src/tools/run-make-support/src/lib.rs
@@ -321,8 +321,9 @@ pub fn set_host_rpath(cmd: &mut Command) {
 /// Read the contents of a file that cannot simply be read by
 /// read_to_string, due to invalid utf8 data, then assert that it contains `expected`.
 #[track_caller]
-pub fn invalid_utf8_contains<P: AsRef<Path>>(path: P, expected: &str) {
+pub fn invalid_utf8_contains<P: AsRef<Path>, S: AsRef<str>>(path: P, expected: S) {
     let buffer = fs_wrapper::read(path.as_ref());
+    let expected = expected.as_ref();
     if !String::from_utf8_lossy(&buffer).contains(expected) {
         eprintln!("=== FILE CONTENTS (LOSSY) ===");
         eprintln!("{}", String::from_utf8_lossy(&buffer));
@@ -335,8 +336,9 @@ pub fn invalid_utf8_contains<P: AsRef<Path>>(path: P, expected: &str) {
 /// Read the contents of a file that cannot simply be read by
 /// read_to_string, due to invalid utf8 data, then assert that it does not contain `expected`.
 #[track_caller]
-pub fn invalid_utf8_not_contains<P: AsRef<Path>>(path: P, expected: &str) {
+pub fn invalid_utf8_not_contains<P: AsRef<Path>, S: AsRef<str>>(path: P, expected: S) {
     let buffer = fs_wrapper::read(path.as_ref());
+    let expected = expected.as_ref();
     if String::from_utf8_lossy(&buffer).contains(expected) {
         eprintln!("=== FILE CONTENTS (LOSSY) ===");
         eprintln!("{}", String::from_utf8_lossy(&buffer));
diff --git a/src/tools/run-make-support/src/rustc.rs b/src/tools/run-make-support/src/rustc.rs
index 3f23c1b8f9e76..054836e87cfbc 100644
--- a/src/tools/run-make-support/src/rustc.rs
+++ b/src/tools/run-make-support/src/rustc.rs
@@ -86,7 +86,8 @@ impl Rustc {
     }
 
     /// Specify type(s) of output files to generate.
-    pub fn emit(&mut self, kinds: &str) -> &mut Self {
+    pub fn emit<S: AsRef<str>>(&mut self, kinds: S) -> &mut Self {
+        let kinds = kinds.as_ref();
         self.cmd.arg(format!("--emit={kinds}"));
         self
     }
diff --git a/tests/run-make/emit-named-files/rmake.rs b/tests/run-make/emit-named-files/rmake.rs
index 79c3ee90c9875..a02c97fec4cba 100644
--- a/tests/run-make/emit-named-files/rmake.rs
+++ b/tests/run-make/emit-named-files/rmake.rs
@@ -4,7 +4,7 @@ use run_make_support::{fs_wrapper, rustc};
 
 fn emit_and_check(out_dir: &Path, out_file: &str, format: &str) {
     let out_file = out_dir.join(out_file);
-    rustc().input("foo.rs").emit(&format!("{format}={}", out_file.display())).run();
+    rustc().input("foo.rs").emit(format!("{format}={}", out_file.display())).run();
     assert!(out_file.is_file());
 }