diff --git a/sshfs/spec.py b/sshfs/spec.py
index f8f5940..177675c 100644
--- a/sshfs/spec.py
+++ b/sshfs/spec.py
@@ -261,6 +261,15 @@ async def _get_file(
 
     @wrap_exceptions
     async def _cp_file(self, lpath, rpath, **kwargs):
+        # Server-side copy through the copy-data extension (asyncssh >=
+        # 2.19 with an OpenSSH >= 9.0 server) needs no shell access and
+        # keeps the data on the server. remote_only guards against
+        # asyncssh silently copying through the client instead. Without
+        # the extension, fall back to a shell cp.
+        async with self._pool.get() as channel:
+            if getattr(channel, "supports_remote_copy", False):
+                return await channel.copy(lpath, rpath, remote_only=True)
+
         cmd = f"cp {shlex.quote(lpath)} {shlex.quote(rpath)}"
         await self._execute(cmd)
 
diff --git a/tests/test_sshfs.py b/tests/test_sshfs.py
index 141baf7..1359412 100644
--- a/tests/test_sshfs.py
+++ b/tests/test_sshfs.py
@@ -211,6 +211,66 @@ def test_copy(fs, remote_dir):
     assert strip_keys(initial_info) == strip_keys(secondary_info)
 
 
+class _FakeChannelPool:
+    def __init__(self, channel):
+        self.channel = channel
+
+    def get(self):
+        pool = self
+
+        class _Ctx:
+            async def __aenter__(self):
+                return pool.channel
+
+            async def __aexit__(self, *exc):
+                return False
+
+        return _Ctx()
+
+
+def test_cp_file_remote_copy(fs, monkeypatch):
+    # A channel advertising copy-data must be used with remote_only=True
+    # (otherwise asyncssh silently copies through the client) and the
+    # shell fallback must not run.
+    calls = {}
+
+    class Channel:
+        supports_remote_copy = True
+
+        async def copy(self, lpath, rpath, remote_only=False):
+            calls["copy"] = (lpath, rpath, remote_only)
+
+    async def no_shell(*args, **kwargs):
+        raise AssertionError("shell fallback must not run")
+
+    monkeypatch.setattr(fs, "_pool", _FakeChannelPool(Channel()))
+    monkeypatch.setattr(fs, "_execute", no_shell)
+
+    fs.cp_file("/src", "/dst")
+    assert calls["copy"] == ("/src", "/dst", True)
+
+
+def test_cp_file_shell_fallback(fs, monkeypatch):
+    # Without copy-data support (or on asyncssh < 2.19, where the
+    # attribute does not exist), the shell cp path is used.
+    calls = {}
+
+    class Channel:
+        supports_remote_copy = False
+
+        async def copy(self, *args, **kwargs):
+            raise AssertionError("copy-data must not be attempted")
+
+    async def record_shell(cmd, **kwargs):
+        calls["cmd"] = cmd
+
+    monkeypatch.setattr(fs, "_pool", _FakeChannelPool(Channel()))
+    monkeypatch.setattr(fs, "_execute", record_shell)
+
+    fs.cp_file("/src", "/dst")
+    assert calls["cmd"] == "cp /src /dst"
+
+
 def test_rm(fs, remote_dir):
     fs.touch(remote_dir + "/a.txt")
     fs.rm(remote_dir + "/a.txt")