diff --git a/src/tools/run-make-support/src/command.rs b/src/tools/run-make-support/src/command.rs
index 0a1bd9b0b34f5..ee651704c6fd0 100644
--- a/src/tools/run-make-support/src/command.rs
+++ b/src/tools/run-make-support/src/command.rs
@@ -185,14 +185,14 @@ impl CompletedProcess {
     /// Checks that `stdout` does not contain `unexpected`.
     #[track_caller]
     pub fn assert_stdout_not_contains<S: AsRef<str>>(&self, unexpected: S) -> &Self {
-        assert_not_contains(&self.stdout_utf8(), unexpected.as_ref());
+        assert_not_contains(&self.stdout_utf8(), unexpected);
         self
     }
 
     /// Checks that `stdout` contains `expected`.
     #[track_caller]
     pub fn assert_stdout_contains<S: AsRef<str>>(&self, expected: S) -> &Self {
-        assert_contains(&self.stdout_utf8(), expected.as_ref());
+        assert_contains(&self.stdout_utf8(), expected);
         self
     }
 
@@ -206,14 +206,14 @@ impl CompletedProcess {
     /// Checks that `stderr` contains `expected`.
     #[track_caller]
     pub fn assert_stderr_contains<S: AsRef<str>>(&self, expected: S) -> &Self {
-        assert_contains(&self.stderr_utf8(), expected.as_ref());
+        assert_contains(&self.stderr_utf8(), expected);
         self
     }
 
     /// Checks that `stderr` does not contain `unexpected`.
     #[track_caller]
     pub fn assert_stderr_not_contains<S: AsRef<str>>(&self, unexpected: S) -> &Self {
-        assert_not_contains(&self.stdout_utf8(), unexpected.as_ref());
+        assert_not_contains(&self.stdout_utf8(), unexpected);
         self
     }
 
diff --git a/src/tools/run-make-support/src/lib.rs b/src/tools/run-make-support/src/lib.rs
index df417722e024f..294dae109425f 100644
--- a/src/tools/run-make-support/src/lib.rs
+++ b/src/tools/run-make-support/src/lib.rs
@@ -409,7 +409,9 @@ pub fn read_dir<F: FnMut(&Path)>(dir: impl AsRef<Path>, mut callback: F) {
 
 /// Check that `actual` is equal to `expected`. Panic otherwise.
 #[track_caller]
-pub fn assert_equals(actual: &str, expected: &str) {
+pub fn assert_equals<S1: AsRef<str>, S2: AsRef<str>>(actual: S1, expected: S2) {
+    let actual = actual.as_ref();
+    let expected = expected.as_ref();
     if actual != expected {
         eprintln!("=== ACTUAL TEXT ===");
         eprintln!("{}", actual);
@@ -421,7 +423,9 @@ pub fn assert_equals(actual: &str, expected: &str) {
 
 /// Check that `haystack` contains `needle`. Panic otherwise.
 #[track_caller]
-pub fn assert_contains(haystack: &str, needle: &str) {
+pub fn assert_contains<S1: AsRef<str>, S2: AsRef<str>>(haystack: S1, needle: S2) {
+    let haystack = haystack.as_ref();
+    let needle = needle.as_ref();
     if !haystack.contains(needle) {
         eprintln!("=== HAYSTACK ===");
         eprintln!("{}", haystack);
@@ -433,7 +437,9 @@ pub fn assert_contains(haystack: &str, needle: &str) {
 
 /// Check that `haystack` does not contain `needle`. Panic otherwise.
 #[track_caller]
-pub fn assert_not_contains(haystack: &str, needle: &str) {
+pub fn assert_not_contains<S1: AsRef<str>, S2: AsRef<str>>(haystack: S1, needle: S2) {
+    let haystack = haystack.as_ref();
+    let needle = needle.as_ref();
     if haystack.contains(needle) {
         eprintln!("=== HAYSTACK ===");
         eprintln!("{}", haystack);
diff --git a/src/tools/run-make-support/src/rustc.rs b/src/tools/run-make-support/src/rustc.rs
index df843d74fc927..3f23c1b8f9e76 100644
--- a/src/tools/run-make-support/src/rustc.rs
+++ b/src/tools/run-make-support/src/rustc.rs
@@ -201,7 +201,8 @@ impl Rustc {
     }
 
     /// Specify the target triple, or a path to a custom target json spec file.
-    pub fn target(&mut self, target: &str) -> &mut Self {
+    pub fn target<S: AsRef<str>>(&mut self, target: S) -> &mut Self {
+        let target = target.as_ref();
         self.cmd.arg(format!("--target={target}"));
         self
     }
diff --git a/src/tools/run-make-support/src/rustdoc.rs b/src/tools/run-make-support/src/rustdoc.rs
index fb00427b1c199..2be962ad88828 100644
--- a/src/tools/run-make-support/src/rustdoc.rs
+++ b/src/tools/run-make-support/src/rustdoc.rs
@@ -104,7 +104,8 @@ impl Rustdoc {
     }
 
     /// Specify the target triple, or a path to a custom target json spec file.
-    pub fn target(&mut self, target: &str) -> &mut Self {
+    pub fn target<S: AsRef<str>>(&mut self, target: S) -> &mut Self {
+        let target = target.as_ref();
         self.cmd.arg(format!("--target={target}"));
         self
     }
diff --git a/tests/run-make/comment-section/rmake.rs b/tests/run-make/comment-section/rmake.rs
index 41df04da7a578..188c6dcb25d2e 100644
--- a/tests/run-make/comment-section/rmake.rs
+++ b/tests/run-make/comment-section/rmake.rs
@@ -21,7 +21,7 @@ fn main() {
         .stdin("fn main() {}")
         .emit("link,obj")
         .arg("-Csave-temps")
-        .target(&target)
+        .target(target)
         .run();
 
     // Check linked output has a `.comment` section with the expected content.
diff --git a/tests/run-make/compressed-debuginfo/rmake.rs b/tests/run-make/compressed-debuginfo/rmake.rs
index 9c6d50ab243cd..58eb2d6b1b39d 100644
--- a/tests/run-make/compressed-debuginfo/rmake.rs
+++ b/tests/run-make/compressed-debuginfo/rmake.rs
@@ -23,8 +23,8 @@ fn check_compression(compression: &str, to_find: &str) {
             cmd("readelf").arg("-t").arg("foo.o").run().assert_stdout_contains(to_find);
         } else {
             assert_contains(
-                &stderr,
-                &format!("unknown debuginfo compression algorithm {compression}"),
+                stderr,
+                format!("unknown debuginfo compression algorithm {compression}"),
             );
         }
     });
diff --git a/tests/run-make/inaccessible-temp-dir/rmake.rs b/tests/run-make/inaccessible-temp-dir/rmake.rs
index c6bfae4cc01db..6b3e9e0b29e38 100644
--- a/tests/run-make/inaccessible-temp-dir/rmake.rs
+++ b/tests/run-make/inaccessible-temp-dir/rmake.rs
@@ -28,7 +28,7 @@ fn main() {
         // Run rustc with `-Z temps-dir` set to a directory *inside* the inaccessible one,
         // so that it can't create `tmp`.
         rustc()
-            .target(&target())
+            .target(target())
             .input("program.rs")
             .arg("-Ztemps-dir=inaccessible/tmp")
             .run_fail()
diff --git a/tests/run-make/static-pie/rmake.rs b/tests/run-make/static-pie/rmake.rs
index 77c5e253bc03a..6a92f92328eec 100644
--- a/tests/run-make/static-pie/rmake.rs
+++ b/tests/run-make/static-pie/rmake.rs
@@ -51,7 +51,7 @@ fn test(compiler: &str) {
 
     rustc()
         .input("test-aslr.rs")
-        .target(&target())
+        .target(target())
         .linker(compiler)
         .arg("-Clinker-flavor=gcc")
         .arg("-Ctarget-feature=+crt-static")