diff --git a/library/alloc/tests/boxed.rs b/library/alloc/tests/boxed.rs
index df13b36e778..6a83f5da87c 100644
--- a/library/alloc/tests/boxed.rs
+++ b/library/alloc/tests/boxed.rs
@@ -1,3 +1,4 @@
+use std::cell::Cell;
 use std::mem::MaybeUninit;
 use std::ptr::NonNull;
 
@@ -52,8 +53,6 @@ fn box_clone_from_ptr_stability() {
 
 #[test]
 fn box_deref_lval() {
-    use std::cell::Cell;
-
     let x = Box::new(Cell::new(5));
     x.set(1000);
     assert_eq!(x.get(), 1000);
diff --git a/library/alloc/tests/fmt.rs b/library/alloc/tests/fmt.rs
index 6fd6468c3ce..757fddd2418 100644
--- a/library/alloc/tests/fmt.rs
+++ b/library/alloc/tests/fmt.rs
@@ -1,5 +1,4 @@
 #![deny(warnings)]
-#![allow(unused_must_use)]
 
 use std::cell::RefCell;
 use std::fmt::{self, Write};
@@ -241,15 +240,15 @@ fn test_format_macro_interface() {
 #[test]
 fn test_write() {
     let mut buf = String::new();
-    write!(&mut buf, "{}", 3);
+    let _ = write!(&mut buf, "{}", 3);
     {
         let w = &mut buf;
-        write!(w, "{foo}", foo = 4);
-        write!(w, "{}", "hello");
-        writeln!(w, "{}", "line");
-        writeln!(w, "{foo}", foo = "bar");
-        w.write_char('☃');
-        w.write_str("str");
+        let _ = write!(w, "{foo}", foo = 4);
+        let _ = write!(w, "{}", "hello");
+        let _ = writeln!(w, "{}", "line");
+        let _ = writeln!(w, "{foo}", foo = "bar");
+        let _ = w.write_char('☃');
+        let _ = w.write_str("str");
     }
 
     t!(buf, "34helloline\nbar\n☃str");
@@ -273,9 +272,9 @@ fn test_format_args() {
     let mut buf = String::new();
     {
         let w = &mut buf;
-        write!(w, "{}", format_args!("{}", 1));
-        write!(w, "{}", format_args!("test"));
-        write!(w, "{}", format_args!("{test}", test = 3));
+        let _ = write!(w, "{}", format_args!("{}", 1));
+        let _ = write!(w, "{}", format_args!("test"));
+        let _ = write!(w, "{}", format_args!("{test}", test = 3));
     }
     let s = buf;
     t!(s, "1test3");
diff --git a/library/core/src/fmt/mod.rs b/library/core/src/fmt/mod.rs
index 8558cb5a5e8..c1038ce4260 100644
--- a/library/core/src/fmt/mod.rs
+++ b/library/core/src/fmt/mod.rs
@@ -2238,5 +2238,6 @@ fn fmt(&self, f: &mut Formatter<'_>) -> Result {
     }
 }
 
-// If you expected tests to be here, look instead at the ui/ifmt.rs test,
+// If you expected tests to be here, look instead at the core/tests/fmt.rs file,
 // it's a lot easier than creating all of the rt::Piece structures here.
+// There are also tests in the alloc crate, for those that need allocations.
diff --git a/library/core/tests/lib.rs b/library/core/tests/lib.rs
index 4211d0e95a9..4db391f3e56 100644
--- a/library/core/tests/lib.rs
+++ b/library/core/tests/lib.rs
@@ -78,7 +78,6 @@
 mod num;
 mod ops;
 mod option;
-mod panic_safe;
 mod pattern;
 mod ptr;
 mod result;
diff --git a/library/core/tests/option.rs b/library/core/tests/option.rs
index bd9a5a6a2cd..ae814efec20 100644
--- a/library/core/tests/option.rs
+++ b/library/core/tests/option.rs
@@ -1,3 +1,4 @@
+use core::cell::Cell;
 use core::clone::Clone;
 use core::mem;
 use core::ops::DerefMut;
@@ -375,8 +376,6 @@ fn option_const() {
 
 #[test]
 fn test_unwrap_drop() {
-    use std::cell::Cell;
-
     struct Dtor<'a> {
         x: &'a Cell<isize>,
     }
diff --git a/library/core/tests/slice.rs b/library/core/tests/slice.rs
index d66d17c1c85..5ef30b1a889 100644
--- a/library/core/tests/slice.rs
+++ b/library/core/tests/slice.rs
@@ -1,3 +1,4 @@
+use core::cell::Cell;
 use core::result::Result::{Err, Ok};
 
 #[test]
@@ -1983,8 +1984,6 @@ fn test_is_sorted() {
 
 #[test]
 fn test_slice_run_destructors() {
-    use core::cell::Cell;
-
     // Make sure that destructors get run on slice literals
     struct Foo<'a> {
         x: &'a Cell<isize>,
diff --git a/library/std/src/panic.rs b/library/std/src/panic.rs
index 18d9c2f11b5..4281867314c 100644
--- a/library/std/src/panic.rs
+++ b/library/std/src/panic.rs
@@ -411,3 +411,6 @@ pub fn catch_unwind<F: FnOnce() -> R + UnwindSafe, R>(f: F) -> Result<R> {
 pub fn resume_unwind(payload: Box<dyn Any + Send>) -> ! {
     panicking::rust_panic_without_hook(payload)
 }
+
+#[cfg(test)]
+mod tests;
diff --git a/library/core/tests/panic_safe.rs b/library/std/src/panic/tests.rs
similarity index 86%
rename from library/core/tests/panic_safe.rs
rename to library/std/src/panic/tests.rs
index 3104ba539c3..b37d74011cc 100644
--- a/library/core/tests/panic_safe.rs
+++ b/library/std/src/panic/tests.rs
@@ -1,9 +1,9 @@
 #![allow(dead_code)]
 
-use std::cell::RefCell;
-use std::panic::{AssertUnwindSafe, UnwindSafe};
-use std::rc::Rc;
-use std::sync::{Arc, Mutex, RwLock};
+use crate::cell::RefCell;
+use crate::panic::{AssertUnwindSafe, UnwindSafe};
+use crate::rc::Rc;
+use crate::sync::{Arc, Mutex, RwLock};
 
 struct Foo {
     a: i32,
@@ -12,7 +12,7 @@ struct Foo {
 fn assert<T: UnwindSafe + ?Sized>() {}
 
 #[test]
-fn test_panic_safety_traits() {
+fn panic_safety_traits() {
     assert::<i32>();
     assert::<&i32>();
     assert::<*mut i32>();