diff --git a/doc/configuration.txt b/doc/configuration.txt
index fc1525728..ef79c9be7 100644
--- a/doc/configuration.txt
+++ b/doc/configuration.txt
@@ -4211,6 +4211,10 @@ tune.h1.be.glitches-threshold <number>
   probably be in the hundreds or thousands to be effective without affecting
   slightly bogus servers. It is also possible to only kill connections when the
   CPU usage crosses a certain level, by using "tune.glitches.kill.cpu-usage".
+  Note that a graceful close is attempted at 75% of the configured threshold by
+  advertising a GOAWAY for a future stream. This ensures that a slightly faulty
+  connection will stop being used after some time without risking to interrupt
+  ongoing transfers.
 
   See also: tune.h1.fe.glitches-threshold, bc_glitches, and
             tune.glitches.kill.cpu-usage
@@ -4226,6 +4230,11 @@ tune.h1.fe.glitches-threshold <number>
   probably be in the hundreds or thousands to be effective without affecting
   slightly bogus clients. It is also possible to only kill connections when the
   CPU usage crosses a certain level, by using "tune.glitches.kill.cpu-usage".
+  Note that a graceful close is attempted at 75% of the configured threshold by
+  advertising a GOAWAY for a future stream. This ensures that a slightly non-
+  compliant client will have the opportunity to create a new connection and
+  continue to work unaffected without ever triggering the hard close thus
+  risking to interrupt ongoing transfers.
 
   See also: tune.h1.be.glitches-threshold, fc_glitches, and
             tune.glitches.kill.cpu-usage
diff --git a/src/mux_h1.c b/src/mux_h1.c
index 6dc809aa8..8e80af974 100644
--- a/src/mux_h1.c
+++ b/src/mux_h1.c
@@ -525,10 +525,20 @@ static inline int _h1_report_glitch(struct h1c *h1c, int increment)
 		h1_be_glitches_threshold : h1_fe_glitches_threshold;
 
 	h1c->glitches += increment;
-	if (thres && h1c->glitches >= thres &&
-	    (th_ctx->idle_pct <= global.tune.glitch_kill_maxidle)) {
-		h1c->flags |= H1C_F_ERROR;
-		return 1;
+	if (unlikely(thres && h1c->glitches >= (thres * 3 + 1) / 4)) {
+		/* at 75% of the threshold, we switch to close mode
+		 * to force clients to periodically reconnect.
+		 */
+		h1c->h1s->flags = (h1c->h1s->flags & ~H1S_F_WANT_MSK) | H1S_F_WANT_CLO;
+
+		/* at 100% of the threshold and excess of CPU usage we also
+		 * actively kill the connection.
+		 */
+		if (h1c->glitches >= thres &&
+		    (th_ctx->idle_pct <= global.tune.glitch_kill_maxidle)) {
+			h1c->flags |= H1C_F_ERROR;
+			return 1;
+		}
 	}
 	return 0;
 }