diff --git a/lib/conncache.c b/lib/conncache.c
index 01681d4ebbc9..4ee276246f0c 100644
--- a/lib/conncache.c
+++ b/lib/conncache.c
@@ -947,11 +947,19 @@ bool Curl_cpool_conn_seems_healthy(struct connectdata *conn,
 {
   struct Curl_easy *admin;
   bool healthy = TRUE;
+  bool poll_input;
 
   DEBUGASSERT(!data->conn);
   if(!CONN_INUSE(conn) && cpool_conn_maxage(data, conn, pnow)) /* too old? */
     return FALSE;
-  if(curlx_ptimediff_ms(pnow, &conn->lastchecked) < 1000)
+
+  /* An idle, non-multiplexed connection must not be reused when it has
+   * input pending (RFC 9112, section 9.2), so that is polled on every
+   * reuse. The once a second limit only applies to the other checks. */
+  poll_input = !CONN_INUSE(conn) && !conn->bits.connect_only &&
+    !Curl_conn_is_multiplex(conn, FIRSTSOCKET) &&
+    !conn->scheme->run->connection_is_dead;
+  if(!poll_input && curlx_ptimediff_ms(pnow, &conn->lastchecked) < 1000)
     return TRUE;
 
   admin = Curl_get_admin(data);
@@ -966,8 +974,7 @@ bool Curl_cpool_conn_seems_healthy(struct connectdata *conn,
     Curl_attach_connection(admin, conn, FALSE);
     healthy = Curl_conn_is_alive(admin, conn, &input_pending);
     Curl_detach_connection(admin);
-    if(healthy && input_pending &&
-       !CONN_INUSE(conn) && !Curl_conn_is_multiplex(conn, FIRSTSOCKET)) {
+    if(healthy && input_pending && poll_input) {
       /* Non-multiplexed connections without attached transfers should
        * not have input pending. The input might be a TLS Notify Close,
        * for all we know. */
diff --git a/tests/data/Makefile.am b/tests/data/Makefile.am
index 3b32fce7bb30..2266010d868d 100644
--- a/tests/data/Makefile.am
+++ b/tests/data/Makefile.am
@@ -1709,6 +1709,7 @@ TESTCASES = \
   test1686 \
   \
   test1700 \
+  test1701 \
   test1702 \
   test1703 \
   test1704 \
diff --git a/tests/data/test1701 b/tests/data/test1701
new file mode 100644
index 000000000000..e4e3d044302a
--- /dev/null
+++ b/tests/data/test1701
@@ -0,0 +1,75 @@
+<?xml version="1.0" encoding="US-ASCII"?>
+<testcase>
+<info>
+<keywords>
+HTTP
+HTTP GET
+DELAY
+</keywords>
+</info>
+# Server-side
+<reply>
+# the first response is exactly 60 bytes so that with writedelay the server
+# sends it in three 20 byte writes and the unsolicited second response only
+# starts arriving after the first transfer is complete and the connection
+# has been returned to the pool
+<data nocheck="yes">
+HTTP/1.1 200 OK
+Funny-head: yesyes
+Content-Length: 6
+
+first
+HTTP/1.1 200 OK
+Content-Length: 6
+
+stray
+</data>
+<data2>
+HTTP/1.1 200 OK
+Content-Length: 7
+
+second
+</data2>
+<servercmd>
+writedelay: 150
+</servercmd>
+</reply>
+
+# Client-side
+<client>
+<server>
+http
+</server>
+<name>
+HTTP/1.1 idle connection with unsolicited data is not reused
+</name>
+# --rate 1/s starts the second request 1000 ms after the first one started,
+# which is about 700 ms after the first response completed and the
+# connection went back to the pool, inside the one second window where the
+# pool used to skip the alive check. The stray response has fully arrived
+# about 750 ms in.
+<command option="no-include">
+http://%HOSTIP:%HTTPPORT/%TESTNUMBER http://%HOSTIP:%HTTPPORT/%TESTNUMBER0002 --rate 1/s
+</command>
+</client>
+
+# Verify data after the test has been "shot"
+<verify>
+<protocol crlf="yes">
+GET /%TESTNUMBER HTTP/1.1
+Host: %HOSTIP:%HTTPPORT
+User-Agent: curl/%VERSION
+Accept: */*
+
+GET /%TESTNUMBER0002 HTTP/1.1
+Host: %HOSTIP:%HTTPPORT
+User-Agent: curl/%VERSION
+Accept: */*
+
+</protocol>
+<stdout>
+first
+second
+</stdout>
+</verify>
+</testcase>