diff --git a/clikernel/core.py b/clikernel/core.py
index 0266a69..4d58788 100644
--- a/clikernel/core.py
+++ b/clikernel/core.py
@@ -151,7 +151,10 @@ async def execute_outs(self:Client, code):
     "Run `code` in the current kernel; nbformat-style output dicts (or a protocol note string)"
     if not self.kc: return 'no kernel: call `connect` first'
     try: return await self.kc.run(code)
-    except DeadKernelError: return 'NOTE: the kernel process died. `connect` to create or attach to another.'
+    except DeadKernelError:
+        await self.kc.aclose()
+        self.kc = None
+        return 'NOTE: the kernel process died. The next `execute` will create another, or call `connect` to attach to one.'
 
 @patch
 async def execute(self:Client, code):
diff --git a/nbs/00_core.ipynb b/nbs/00_core.ipynb
index 57bb706..b383268 100644
--- a/nbs/00_core.ipynb
+++ b/nbs/00_core.ipynb
@@ -308,7 +308,10 @@
     "    \"Run `code` in the current kernel; nbformat-style output dicts (or a protocol note string)\"\n",
     "    if not self.kc: return 'no kernel: call `connect` first'\n",
     "    try: return await self.kc.run(code)\n",
-    "    except DeadKernelError: return 'NOTE: the kernel process died. `connect` to create or attach to another.'\n",
+    "    except DeadKernelError:\n",
+    "        await self.kc.aclose()\n",
+    "        self.kc = None\n",
+    "        return 'NOTE: the kernel process died. The next `execute` will create another, or call `connect` to attach to one.'\n",
     "\n",
     "@patch\n",
     "async def execute(self:Client, code):\n",
@@ -634,6 +637,7 @@
     "await c2.mgr.shutdown_kernel(c2.kid)   # killed behind our back\n",
     "res = await c2.execute('1+1')\n",
     "assert res.startswith('NOTE')          # a concise note, not a traceback\n",
+    "assert c2.kc is None                    # the next execute can auto-connect instead of reusing a dead ws\n",
     "await c2.connect()\n",
     "test_eq(await c2.execute('1+1'), '2')  # and connecting again recovers\n",
     "await c2.stop()"