diff --git a/sshd/sshd.go b/sshd/sshd.go
index 59d315d..3508718 100644
--- a/sshd/sshd.go
+++ b/sshd/sshd.go
@@ -18,6 +18,7 @@ import (
 	"os"
 	"path/filepath"
 	"sync"
+	"sync/atomic"
 	"time"
 
 	"golang.org/x/crypto/ssh"
@@ -143,9 +144,14 @@ func (s *Server) Serve(ctx context.Context, ln net.Listener) error {
 func (s *Server) handle(ctx context.Context, nc net.Conn) {
 	defer nc.Close()
 	nc.SetDeadline(time.Now().Add(handshakeTimeout))
-	conn, chans, reqs, err := ssh.NewServerConn(nc, s.conf)
+	rc := &readCounter{Conn: nc}
+	conn, chans, reqs, err := ssh.NewServerConn(rc, s.conf)
 	if err != nil {
-		s.cfg.Logf("ssh: sign-in from %s failed: %v", nc.RemoteAddr(), err)
+		// A client that connects and never says anything is a port probe or a health check (Hammerhead
+		// checks every TCP resource this way), not a failed sign-in, so it is not worth a log line each time.
+		if rc.n.Load() > 0 {
+			s.cfg.Logf("ssh: sign-in from %s failed: %v", nc.RemoteAddr(), err)
+		}
 		return
 	}
 	nc.SetDeadline(time.Time{})
@@ -172,6 +178,18 @@ func (s *Server) handle(ctx context.Context, nc net.Conn) {
 	wg.Wait()
 }
 
+// readCounter counts the bytes a client has sent.
+type readCounter struct {
+	net.Conn
+	n atomic.Int64
+}
+
+func (r *readCounter) Read(p []byte) (int, error) {
+	n, err := r.Conn.Read(p)
+	r.n.Add(int64(n))
+	return n, err
+}
+
 type ptyReq struct {
 	term       string
 	cols, rows uint32
diff --git a/sshd/sshd_test.go b/sshd/sshd_test.go
index cca3aca..77758d9 100644
--- a/sshd/sshd_test.go
+++ b/sshd/sshd_test.go
@@ -4,9 +4,12 @@ import (
 	"context"
 	"crypto/ed25519"
 	"crypto/rand"
+	"fmt"
 	"net"
 	"os"
 	"path/filepath"
+	"strings"
+	"sync"
 	"testing"
 	"time"
 
@@ -148,3 +151,50 @@ func TestNoForwarding(t *testing.T) {
 		t.Fatal("port forwarding was allowed")
 	}
 }
+
+// Hammerhead health-checks a TCP resource by connecting and hanging up; that must not look like
+// a failed sign-in in the log, while a real failure still does.
+func TestProbesAreNotLogged(t *testing.T) {
+	good := newSigner(t)
+	dir := t.TempDir()
+	keys := filepath.Join(dir, "authorized_keys")
+	if err := os.WriteFile(keys, []byte(authLine(good)), 0o600); err != nil {
+		t.Fatal(err)
+	}
+	var mu sync.Mutex
+	var logs []string
+	srv, err := New(Config{AuthorizedKeys: keys, HostKey: filepath.Join(dir, "host_key"), Logf: func(f string, a ...any) {
+		mu.Lock()
+		logs = append(logs, fmt.Sprintf(f, a...))
+		mu.Unlock()
+	}})
+	if err != nil {
+		t.Fatal(err)
+	}
+	ln, err := net.Listen("tcp", "127.0.0.1:0")
+	if err != nil {
+		t.Fatal(err)
+	}
+	ctx, cancel := context.WithCancel(context.Background())
+	done := make(chan struct{})
+	go func() { srv.Serve(ctx, ln); close(done) }()
+	t.Cleanup(func() { cancel(); <-done })
+
+	for i := 0; i < 3; i++ {
+		c, err := net.Dial("tcp", ln.Addr().String())
+		if err != nil {
+			t.Fatal(err)
+		}
+		c.Close()
+	}
+	time.Sleep(200 * time.Millisecond)
+	if _, err := dial(ln.Addr().String(), ssh.PublicKeys(newSigner(t))); err == nil {
+		t.Fatal("an unknown key signed in")
+	}
+	time.Sleep(200 * time.Millisecond)
+	mu.Lock()
+	defer mu.Unlock()
+	if len(logs) != 1 || !strings.Contains(logs[0], "failed") {
+		t.Fatalf("want exactly the one real failure logged, got %q", logs)
+	}
+}