diff --git a/tests/by-util/test_cp.rs b/tests/by-util/test_cp.rs
index 156daec1f15..7a0889b0fa6 100644
--- a/tests/by-util/test_cp.rs
+++ b/tests/by-util/test_cp.rs
@@ -8,6 +8,7 @@ use crate::common::util::TestScenario;
 #[cfg(not(windows))]
 use std::fs::set_permissions;
 
+use std::io::Write;
 #[cfg(not(windows))]
 use std::os::unix::fs;
 
@@ -447,9 +448,9 @@ fn test_cp_arg_update_older_dest_older_than_src() {
     let old_content = "old content\n";
     let new_content = "new content\n";
 
-    at.write(old, old_content);
-
-    sleep(Duration::from_secs(1));
+    let mut f = at.make_file(old);
+    f.write_all(old_content.as_bytes()).unwrap();
+    f.set_modified(std::time::UNIX_EPOCH).unwrap();
 
     at.write(new, new_content);
 
@@ -473,9 +474,9 @@ fn test_cp_arg_update_short_no_overwrite() {
     let old_content = "old content\n";
     let new_content = "new content\n";
 
-    at.write(old, old_content);
-
-    sleep(Duration::from_secs(1));
+    let mut f = at.make_file(old);
+    f.write_all(old_content.as_bytes()).unwrap();
+    f.set_modified(std::time::UNIX_EPOCH).unwrap();
 
     at.write(new, new_content);
 
@@ -499,9 +500,9 @@ fn test_cp_arg_update_short_overwrite() {
     let old_content = "old content\n";
     let new_content = "new content\n";
 
-    at.write(old, old_content);
-
-    sleep(Duration::from_secs(1));
+    let mut f = at.make_file(old);
+    f.write_all(old_content.as_bytes()).unwrap();
+    f.set_modified(std::time::UNIX_EPOCH).unwrap();
 
     at.write(new, new_content);
 
@@ -526,9 +527,9 @@ fn test_cp_arg_update_none_then_all() {
     let old_content = "old content\n";
     let new_content = "new content\n";
 
-    at.write(old, old_content);
-
-    sleep(Duration::from_secs(1));
+    let mut f = at.make_file(old);
+    f.write_all(old_content.as_bytes()).unwrap();
+    f.set_modified(std::time::UNIX_EPOCH).unwrap();
 
     at.write(new, new_content);
 
@@ -554,9 +555,9 @@ fn test_cp_arg_update_all_then_none() {
     let old_content = "old content\n";
     let new_content = "new content\n";
 
-    at.write(old, old_content);
-
-    sleep(Duration::from_secs(1));
+    let mut f = at.make_file(old);
+    f.write_all(old_content.as_bytes()).unwrap();
+    f.set_modified(std::time::UNIX_EPOCH).unwrap();
 
     at.write(new, new_content);