diff --git a/src/uu/cp/src/cp.rs b/src/uu/cp/src/cp.rs
index 2cdd79255..a4d0cff4d 100644
--- a/src/uu/cp/src/cp.rs
+++ b/src/uu/cp/src/cp.rs
@@ -2446,7 +2446,7 @@ fn copy_file(
                 copy_attributes(&src, dest, &options.attributes)?;
             }
         }
-    } else if source_is_stream && source.exists() {
+    } else if source_is_stream && !source.exists() {
         // Some stream files may not exist after we have copied it,
         // like anonymous pipes. Thus, we can't really copy its
         // attributes. However, this is already handled in the stream
diff --git a/tests/by-util/test_cp.rs b/tests/by-util/test_cp.rs
index 8575d1959..730c7a87e 100644
--- a/tests/by-util/test_cp.rs
+++ b/tests/by-util/test_cp.rs
@@ -4,7 +4,7 @@
 // file that was distributed with this source code.
 
 // spell-checker:ignore (flags) reflink (fs) tmpfs (linux) rlimit Rlim NOFILE clob btrfs neve ROOTDIR USERDIR outfile uufs xattrs
-// spell-checker:ignore bdfl hlsl IRWXO IRWXG nconfined matchpathcon libselinux-devel
+// spell-checker:ignore bdfl hlsl IRWXO IRWXG nconfined matchpathcon libselinux-devel prwx
 use uucore::display::Quotable;
 use uutests::util::TestScenario;
 use uutests::{at_and_ucmd, new_ucmd, path_concat, util_name};
@@ -3087,13 +3087,20 @@ fn test_cp_link_backup() {
 fn test_cp_fifo() {
     let (at, mut ucmd) = at_and_ucmd!();
     at.mkfifo("fifo");
-    ucmd.arg("-r")
+    // Also test that permissions are preserved
+    at.set_mode("fifo", 0o731);
+    ucmd.arg("--preserve=mode")
+        .arg("-r")
         .arg("fifo")
         .arg("fifo2")
         .succeeds()
         .no_stderr()
         .no_stdout();
     assert!(at.is_fifo("fifo2"));
+
+    let metadata = std::fs::metadata(at.subdir.join("fifo2")).unwrap();
+    let permission = uucore::fs::display_permissions(&metadata, true);
+    assert_eq!(permission, "prwx-wx--x".to_string());
 }
 
 #[test]