diff --git a/src/tools/tidy/src/allowed_run_make_makefiles.txt b/src/tools/tidy/src/allowed_run_make_makefiles.txt
index 276d2d694cda0..686cc2f9c43e9 100644
--- a/src/tools/tidy/src/allowed_run_make_makefiles.txt
+++ b/src/tools/tidy/src/allowed_run_make_makefiles.txt
@@ -162,9 +162,6 @@ run-make/symbol-mangling-hashed/Makefile
 run-make/symbol-visibility/Makefile
 run-make/symbols-include-type-name/Makefile
 run-make/sysroot-crates-are-unstable/Makefile
-run-make/target-cpu-native/Makefile
-run-make/target-specs/Makefile
-run-make/target-without-atomic-cas/Makefile
 run-make/test-benches/Makefile
 run-make/test-harness/Makefile
 run-make/thumb-none-cortex-m/Makefile
diff --git a/tests/run-make/target-cpu-native/Makefile b/tests/run-make/target-cpu-native/Makefile
deleted file mode 100644
index eb3ca1e13aa62..0000000000000
--- a/tests/run-make/target-cpu-native/Makefile
+++ /dev/null
@@ -1,20 +0,0 @@
-include ../tools.mk
-
-# only-linux
-# only-x86_64
-#
-# I *really* don't want to deal with a cross-platform way to compare file sizes,
-# tests in `make` sort of are awful
-
-all: $(TMPDIR)/out.log
-	# Make sure no warnings about "unknown CPU `native`" were emitted
-	if [ "$$(wc -c $(TMPDIR)/out.log | cut -d' ' -f 1)" = "0" ]; then \
-	  echo no warnings generated; \
-	else \
-	  exit 1; \
-	fi
-
-
-$(TMPDIR)/out.log:
-	$(RUSTC) foo.rs -C target-cpu=native 2>&1 | tee $(TMPDIR)/out.log
-	$(call RUN,foo)
diff --git a/tests/run-make/target-cpu-native/rmake.rs b/tests/run-make/target-cpu-native/rmake.rs
new file mode 100644
index 0000000000000..fd5fb6193fe06
--- /dev/null
+++ b/tests/run-make/target-cpu-native/rmake.rs
@@ -0,0 +1,14 @@
+// target-cpu is a codegen flag that generates code for the processor of the host machine
+// running the compilation. This test is a sanity test that this flag does not cause any
+// warnings when used, and that binaries produced by it can also be successfully executed.
+// See https://github.com/rust-lang/rust/pull/23238
+
+use run_make_support::{run, rustc};
+
+fn main() {
+    let out = rustc().input("foo.rs").arg("-Ctarget-cpu=native").run().stderr_utf8();
+    run("foo");
+    // There should be zero warnings emitted - the bug would cause "unknown CPU `native`"
+    // to be printed out.
+    assert!(out.is_empty());
+}
diff --git a/tests/run-make/target-specs/Makefile b/tests/run-make/target-specs/Makefile
deleted file mode 100644
index 161b66021857b..0000000000000
--- a/tests/run-make/target-specs/Makefile
+++ /dev/null
@@ -1,12 +0,0 @@
-include ../tools.mk
-all:
-	$(RUSTC) foo.rs --target=my-awesome-platform.json --crate-type=lib --emit=asm
-	$(CGREP) -v morestack < $(TMPDIR)/foo.s
-	$(RUSTC) foo.rs --target=my-invalid-platform.json 2>&1 | $(CGREP) "Error loading target specification"
-	$(RUSTC) foo.rs --target=my-incomplete-platform.json 2>&1 | $(CGREP) 'Field llvm-target'
-	RUST_TARGET_PATH=. $(RUSTC) foo.rs --target=my-awesome-platform --crate-type=lib --emit=asm
-	RUST_TARGET_PATH=. $(RUSTC) foo.rs --target=my-x86_64-unknown-linux-gnu-platform --crate-type=lib --emit=asm
-	$(RUSTC) -Z unstable-options --target=my-awesome-platform.json --print target-spec-json > $(TMPDIR)/test-platform.json && $(RUSTC) -Z unstable-options --target=$(TMPDIR)/test-platform.json --print target-spec-json | diff -q $(TMPDIR)/test-platform.json -
-	$(RUSTC) foo.rs --target=definitely-not-builtin-target 2>&1 | $(CGREP) 'may not set is_builtin'
-	$(RUSTC) foo.rs --target=endianness-mismatch 2>&1 | $(CGREP) '"data-layout" claims architecture is little-endian'
-	$(RUSTC) foo.rs --target=mismatching-data-layout --crate-type=lib 2>&1 | $(CGREP) 'data-layout for target'
diff --git a/tests/run-make/target-specs/rmake.rs b/tests/run-make/target-specs/rmake.rs
new file mode 100644
index 0000000000000..d2b5f65083808
--- /dev/null
+++ b/tests/run-make/target-specs/rmake.rs
@@ -0,0 +1,71 @@
+// Target-specific compilation in rustc used to have case-by-case peculiarities in 2014,
+// with the compiler having redundant target types and unspecific names. An overarching rework
+// in #16156 changed the way the target flag functions, and this test attempts compilation
+// with the target flag's bundle of new features to check that compilation either succeeds while
+// using them correctly, or fails with the right error message when using them improperly.
+// See https://github.com/rust-lang/rust/pull/16156
+
+use run_make_support::{diff, fs_wrapper, rustc};
+
+fn main() {
+    rustc().input("foo.rs").target("my-awesome-platform.json").crate_type("lib").emit("asm").run();
+    assert!(!fs_wrapper::read_to_string("foo.s").contains("morestack"));
+    rustc()
+        .input("foo.rs")
+        .target("my-invalid-platform.json")
+        .run_fail()
+        .assert_stderr_contains("Error loading target specification");
+    rustc()
+        .input("foo.rs")
+        .target("my-incomplete-platform.json")
+        .run_fail()
+        .assert_stderr_contains("Field llvm-target");
+    rustc()
+        .env("RUST_TARGET_PATH", ".")
+        .input("foo.rs")
+        .target("my-awesome-platform")
+        .crate_type("lib")
+        .emit("asm")
+        .run();
+    rustc()
+        .env("RUST_TARGET_PATH", ".")
+        .input("foo.rs")
+        .target("my-x86_64-unknown-linux-gnu-platform")
+        .crate_type("lib")
+        .emit("asm")
+        .run();
+    let test_platform = rustc()
+        .arg("-Zunstable-options")
+        .target("my-awesome-platform.json")
+        .print("target-spec-json")
+        .run()
+        .stdout_utf8();
+    fs_wrapper::create_file("test-platform.json");
+    fs_wrapper::write("test-platform.json", test_platform.as_bytes());
+    let test_platform_2 = rustc()
+        .arg("-Zunstable-options")
+        .target("test-platform.json")
+        .print("target-spec-json")
+        .run()
+        .stdout_utf8();
+    diff()
+        .expected_file("test-platform.json")
+        .actual_text("test-platform-2", test_platform_2)
+        .run();
+    rustc()
+        .input("foo.rs")
+        .target("definitely-not-builtin-target")
+        .run_fail()
+        .assert_stderr_contains("may not set is_builtin");
+    rustc()
+        .input("foo.rs")
+        .target("endianness-mismatch")
+        .run_fail()
+        .assert_stderr_contains(r#""data-layout" claims architecture is little-endian"#);
+    rustc()
+        .input("foo.rs")
+        .target("mismatching-data-layout")
+        .crate_type("lib")
+        .run_fail()
+        .assert_stderr_contains("data-layout for target");
+}
diff --git a/tests/run-make/target-without-atomic-cas/Makefile b/tests/run-make/target-without-atomic-cas/Makefile
deleted file mode 100644
index 451f03d66cd23..0000000000000
--- a/tests/run-make/target-without-atomic-cas/Makefile
+++ /dev/null
@@ -1,5 +0,0 @@
-include ../tools.mk
-
-# The target used below doesn't support atomic CAS operations. Verify that's the case
-all:
-	$(RUSTC) --print cfg --target thumbv6m-none-eabi | $(CGREP) -v 'target_has_atomic="ptr"'
diff --git a/tests/run-make/target-without-atomic-cas/rmake.rs b/tests/run-make/target-without-atomic-cas/rmake.rs
new file mode 100644
index 0000000000000..c8782b6d1a566
--- /dev/null
+++ b/tests/run-make/target-without-atomic-cas/rmake.rs
@@ -0,0 +1,16 @@
+// ARM Cortex-M are a class of processors supported by the rust compiler. However,
+// they cannot support any atomic features, such as Arc. This test simply prints
+// the configuration details of one Cortex target, and checks that the compiler
+// does not falsely list atomic support.
+// See https://github.com/rust-lang/rust/pull/36874
+
+use run_make_support::rustc;
+
+// The target used below doesn't support atomic CAS operations. Verify that's the case
+fn main() {
+    rustc()
+        .print("cfg")
+        .target("thumbv6m-none-eabi")
+        .run()
+        .assert_stdout_not_contains(r#"target_has_atomic="ptr""#);
+}