diff --git a/src/uu/cp/src/cp.rs b/src/uu/cp/src/cp.rs
index 6a8649dc179..d45f994180d 100644
--- a/src/uu/cp/src/cp.rs
+++ b/src/uu/cp/src/cp.rs
@@ -1543,7 +1543,9 @@ fn handle_existing_dest(
         return Err(format!("{} and {} are the same file", source.quote(), dest.quote()).into());
     }
 
-    options.overwrite.verify(dest)?;
+    if options.update != UpdateMode::ReplaceIfOlder {
+        options.overwrite.verify(dest)?;
+    }
 
     let backup_path = backup_control::get_backup_path(options.backup, dest, &options.backup_suffix);
     if let Some(backup_path) = backup_path {
@@ -1770,6 +1772,8 @@ fn handle_copy_mode(
                         if src_time <= dest_time {
                             return Ok(());
                         } else {
+                            options.overwrite.verify(dest)?;
+
                             copy_helper(
                                 source,
                                 dest,
@@ -1866,14 +1870,6 @@ fn copy_file(
     copied_files: &mut HashMap<FileInformation, PathBuf>,
     source_in_command_line: bool,
 ) -> CopyResult<()> {
-    if (options.update == UpdateMode::ReplaceIfOlder || options.update == UpdateMode::ReplaceNone)
-        && options.overwrite == OverwriteMode::Interactive(ClobberMode::Standard)
-    {
-        // `cp -i --update old new` when `new` exists doesn't copy anything
-        // and exit with 0
-        return Ok(());
-    }
-
     // Fail if dest is a dangling symlink or a symlink this program created previously
     if dest.is_symlink() {
         if FileInformation::from_path(dest, false)
diff --git a/tests/by-util/test_cp.rs b/tests/by-util/test_cp.rs
index e3b373da19d..bdfc9c8e8a4 100644
--- a/tests/by-util/test_cp.rs
+++ b/tests/by-util/test_cp.rs
@@ -274,20 +274,6 @@ fn test_cp_target_directory_is_file() {
         .stderr_contains(format!("'{TEST_HOW_ARE_YOU_SOURCE}' is not a directory"));
 }
 
-#[test]
-// FixMe: for FreeBSD, flaky test; track repair progress at GH:uutils/coreutils/issue/4725
-#[cfg(not(target_os = "freebsd"))]
-fn test_cp_arg_update_interactive() {
-    new_ucmd!()
-        .arg(TEST_HELLO_WORLD_SOURCE)
-        .arg(TEST_HOW_ARE_YOU_SOURCE)
-        .arg("-i")
-        .arg("--update")
-        .succeeds()
-        .no_stdout()
-        .no_stderr();
-}
-
 #[test]
 fn test_cp_arg_update_interactive_error() {
     new_ucmd!()
@@ -498,7 +484,7 @@ fn test_cp_arg_interactive() {
 
 #[test]
 #[cfg(not(any(target_os = "android", target_os = "freebsd")))]
-fn test_cp_arg_interactive_update() {
+fn test_cp_arg_interactive_update_overwrite_newer() {
     // -u -i won't show the prompt to validate the override or not
     // Therefore, the error code will be 0
     let (at, mut ucmd) = at_and_ucmd!();
@@ -517,12 +503,13 @@ fn test_cp_arg_interactive_update() {
 
 #[test]
 #[cfg(not(any(target_os = "android", target_os = "freebsd")))]
-#[ignore = "known issue #6019"]
-fn test_cp_arg_interactive_update_newer() {
+fn test_cp_arg_interactive_update_overwrite_older() {
     // -u -i *WILL* show the prompt to validate the override.
     // Therefore, the error code depends on the prompt response.
+    // Option N
     let (at, mut ucmd) = at_and_ucmd!();
     at.touch("b");
+    std::thread::sleep(Duration::from_secs(1));
     at.touch("a");
     ucmd.args(&["-i", "-u", "a", "b"])
         .pipe_in("N\n")
@@ -530,6 +517,16 @@ fn test_cp_arg_interactive_update_newer() {
         .code_is(1)
         .no_stdout()
         .stderr_is("cp: overwrite 'b'? ");
+
+    // Option Y
+    let (at, mut ucmd) = at_and_ucmd!();
+    at.touch("b");
+    std::thread::sleep(Duration::from_secs(1));
+    at.touch("a");
+    ucmd.args(&["-i", "-u", "a", "b"])
+        .pipe_in("Y\n")
+        .succeeds()
+        .no_stdout();
 }
 
 #[test]