diff --git a/tests/pass-dep/libc/libc-mem.rs b/tests/pass-dep/libc/libc-mem.rs
index 531d637d1f..7105b076d6 100644
--- a/tests/pass-dep/libc/libc-mem.rs
+++ b/tests/pass-dep/libc/libc-mem.rs
@@ -1,6 +1,10 @@
 #![feature(pointer_is_aligned_to)]
 use std::{mem, ptr, slice};
 
+#[path = "../../utils/mod.rs"]
+mod utils;
+use utils::check_nondet;
+
 fn test_memcpy() {
     unsafe {
         let src = [1i8, 2, 3];
@@ -120,13 +124,12 @@ fn test_memset() {
 }
 
 fn test_malloc() {
-    // Test that small allocations sometimes *are* not very aligned.
-    let saw_unaligned = (0..64).any(|_| unsafe {
+    // Test that small allocations sometimes are *not* very aligned (and sometimes they are).
+    check_nondet(|| unsafe {
         let p = libc::malloc(3);
         libc::free(p);
-        (p as usize) % 4 != 0 // find any that this is *not* 4-aligned
+        (p as usize) % 4 == 0
     });
-    assert!(saw_unaligned);
 
     unsafe {
         let p1 = libc::malloc(20);
diff --git a/tests/pass/dyn-traits.rs b/tests/pass/dyn-traits.rs
index f622012096..47f913adae 100644
--- a/tests/pass/dyn-traits.rs
+++ b/tests/pass/dyn-traits.rs
@@ -1,3 +1,7 @@
+#[path = "../utils/mod.rs"]
+mod utils;
+use utils::check_nondet;
+
 fn ref_box_dyn() {
     struct Struct(i32);
 
@@ -147,7 +151,7 @@ fn vtable_ptr_eq() {
     // We don't always get the same vtable when casting this to a wide pointer.
     let x = &2;
     let x_wide = x as &dyn fmt::Display;
-    assert!((0..256).any(|_| !ptr::eq(x as &dyn fmt::Display, x_wide)));
+    check_nondet(|| ptr::eq(x as &dyn fmt::Display, x_wide));
 }
 
 fn main() {
diff --git a/tests/pass/function_pointers.rs b/tests/pass/function_pointers.rs
index 7145be334a..96f6f2568e 100644
--- a/tests/pass/function_pointers.rs
+++ b/tests/pass/function_pointers.rs
@@ -2,6 +2,10 @@
 
 use std::mem;
 
+#[path = "../utils/mod.rs"]
+mod utils;
+use utils::check_nondet;
+
 trait Answer {
     fn answer() -> Self;
 }
@@ -30,6 +34,7 @@ fn i() -> i32 {
     73
 }
 
+#[inline(never)] // optimizations mask the non-determinism we test for below
 fn return_fn_ptr(f: fn() -> i32) -> fn() -> i32 {
     f
 }
@@ -85,7 +90,7 @@ fn main() {
     assert!(return_fn_ptr(i) as unsafe fn() -> i32 == i as fn() -> i32 as unsafe fn() -> i32);
     // Miri gives different addresses to different reifications of a generic function.
     // at least if we try often enough.
-    assert!((0..256).any(|_| return_fn_ptr(f) != f));
+    check_nondet(|| return_fn_ptr(f) == f);
     // However, if we only turn `f` into a function pointer and use that pointer,
     // it is equal to itself.
     let f2 = f as fn() -> i32;
diff --git a/tests/pass/shims/fs.rs b/tests/pass/shims/fs.rs
index 022dcc5dcb..43fbf6b085 100644
--- a/tests/pass/shims/fs.rs
+++ b/tests/pass/shims/fs.rs
@@ -13,6 +13,7 @@ use std::path::Path;
 
 #[path = "../../utils/mod.rs"]
 mod utils;
+use utils::check_nondet;
 
 fn main() {
     test_path_conversion();
@@ -81,25 +82,25 @@ fn test_file() {
 }
 
 fn test_file_partial_reads_writes() {
-    let path = utils::prepare_with_content("miri_test_fs_file.txt", b"abcdefg");
+    let path1 = utils::prepare_with_content("miri_test_fs_file1.txt", b"abcdefg");
+    let path2 = utils::prepare_with_content("miri_test_fs_file2.txt", b"abcdefg");
 
     // Ensure we sometimes do incomplete writes.
-    let got_short_write = (0..16).any(|_| {
-        let _ = remove_file(&path); // FIXME(win, issue #4483): errors if the file already exists
-        let mut file = File::create(&path).unwrap();
-        file.write(&[0; 4]).unwrap() != 4
+    check_nondet(|| {
+        let _ = remove_file(&path1); // FIXME(win, issue #4483): errors if the file already exists
+        let mut file = File::create(&path1).unwrap();
+        file.write(&[0; 4]).unwrap() == 4
     });
-    assert!(got_short_write);
     // Ensure we sometimes do incomplete reads.
-    let got_short_read = (0..16).any(|_| {
-        let mut file = File::open(&path).unwrap();
+    check_nondet(|| {
+        let mut file = File::open(&path2).unwrap();
         let mut buf = [0; 4];
-        file.read(&mut buf).unwrap() != 4
+        file.read(&mut buf).unwrap() == 4
     });
-    assert!(got_short_read);
 
     // Clean up
-    remove_file(&path).unwrap();
+    remove_file(&path1).unwrap();
+    remove_file(&path2).unwrap();
 }
 
 fn test_file_clone() {
diff --git a/tests/utils/mod.rs b/tests/utils/mod.rs
index 37f9996216..f855f115e4 100644
--- a/tests/utils/mod.rs
+++ b/tests/utils/mod.rs
@@ -55,7 +55,10 @@ pub fn check_all_outcomes<T: Eq + std::hash::Hash + std::fmt::Debug>(
 /// Check that the operation is non-deterministic
 #[track_caller]
 pub fn check_nondet<T: PartialEq + std::fmt::Debug>(f: impl Fn() -> T) {
-    let rounds = 50;
+    // We test some rather unlikely events with this, such as two global allocations getting the
+    // same "salt" (1/32 chance). So give this *many* shots before we consider the test to have
+    // failed.
+    let rounds = 500;
     let first = f();
     for _ in 1..rounds {
         if f() != first {