diff --git a/distributed/comm/core.py b/distributed/comm/core.py
index 7d16bda2336..74246a22d50 100644
--- a/distributed/comm/core.py
+++ b/distributed/comm/core.py
@@ -280,7 +280,7 @@ def time_left():
 
     backoff_base = 0.01
     attempt = 0
-
+    logger.debug("Establishing connection to %s", loc)
     # Prefer multiple small attempts than one long attempt. This should protect
     # primarily from DNS race conditions
     # gh3104, gh4176, gh4167
diff --git a/distributed/core.py b/distributed/core.py
index 96dfe7b68a9..2734b9a0e37 100644
--- a/distributed/core.py
+++ b/distributed/core.py
@@ -443,6 +443,47 @@ def status(self, value: Status) -> None:
             raise TypeError(f"Expected Status; got {value!r}")
         self._status = value
 
+    @property
+    def incoming_comms_open(self) -> int:
+        """The number of total incoming connections listening to remote RPCs"""
+        return len(self._comms)
+
+    @property
+    def incoming_comms_active(self) -> int:
+        """The number of connections currently handling a remote RPC"""
+        return len([c for c, op in self._comms.items() if op is not None])
+
+    @property
+    def outgoing_comms_open(self) -> int:
+        """The number of connections currently open and waiting for a remote RPC"""
+        return self.rpc.open
+
+    @property
+    def outgoing_comms_active(self) -> int:
+        """The number of outgoing connections that are currently used to
+        execute a RPC"""
+        return self.rpc.active
+
+    def get_connection_counters(self) -> dict[str, int]:
+        """A dict with various connection counters
+
+        See also
+        --------
+        Server.incoming_comms_open
+        Server.incoming_comms_active
+        Server.outgoing_comms_open
+        Server.outgoing_comms_active
+        """
+        return {
+            attr: getattr(self, attr)
+            for attr in [
+                "incoming_comms_open",
+                "incoming_comms_active",
+                "outgoing_comms_open",
+                "outgoing_comms_active",
+            ]
+        }
+
     async def finished(self):
         """Wait until the server has finished"""
         await self._event_finished.wait()
diff --git a/distributed/tests/test_core.py b/distributed/tests/test_core.py
index 35e8e748ed7..739cf557a64 100644
--- a/distributed/tests/test_core.py
+++ b/distributed/tests/test_core.py
@@ -1134,11 +1134,71 @@ async def long_handler(comm):
         while not server._comms:
             await asyncio.sleep(0.05)
         assert set(server._comms.values()) == {"wait"}
+
+        assert server.incoming_comms_open == 1
+        assert server.incoming_comms_active == 1
+
+        def validate_dict(server):
+            assert (
+                server.get_connection_counters()["incoming_comms_open"]
+                == server.incoming_comms_open
+            )
+            assert (
+                server.get_connection_counters()["incoming_comms_active"]
+                == server.incoming_comms_active
+            )
+
+            assert (
+                server.get_connection_counters()["outgoing_comms_open"]
+                == server.rpc.open
+            )
+            assert (
+                server.get_connection_counters()["outgoing_comms_active"]
+                == server.rpc.active
+            )
+
+        validate_dict(server)
+
         assert await comm.read() == "done"
         assert set(server._comms.values()) == {None}
+        assert server.incoming_comms_open == 1
+        assert server.incoming_comms_active == 0
+        validate_dict(server)
         await comm.close()
+
         while server._comms:
             await asyncio.sleep(0.01)
+        assert server.incoming_comms_active == 0
+        assert server.incoming_comms_open == 0
+        validate_dict(server)
+
+        async with Server({}) as server2:
+            rpc_ = server2.rpc(server.address)
+            task = asyncio.create_task(rpc_.wait())
+            while not server.incoming_comms_active:
+                await asyncio.sleep(0.1)
+            assert server.incoming_comms_active == 1
+            assert server.incoming_comms_open == 1
+            assert server.outgoing_comms_active == 0
+            assert server.outgoing_comms_open == 0
+
+            assert server2.incoming_comms_active == 0
+            assert server2.incoming_comms_open == 0
+            assert server2.outgoing_comms_active == 1
+            assert server2.outgoing_comms_open == 1
+            validate_dict(server)
+
+            await task
+            assert server.incoming_comms_active == 0
+            assert server.incoming_comms_open == 1
+            assert server.outgoing_comms_active == 0
+            assert server.outgoing_comms_open == 0
+
+            assert server2.incoming_comms_active == 0
+            assert server2.incoming_comms_open == 0
+            assert server2.outgoing_comms_active == 0
+            assert server2.outgoing_comms_open == 1
+            validate_dict(server)
 
 
 @pytest.mark.parametrize("close_via_rpc", [True, False])