diff --git a/prio-queue.c b/prio-queue.c
index ec33ac27db..9748528ce6 100644
--- a/prio-queue.c
+++ b/prio-queue.c
@@ -58,22 +58,10 @@ void prio_queue_put(struct prio_queue *queue, void *thing)
 	}
 }
 
-void *prio_queue_get(struct prio_queue *queue)
+static void sift_down_root(struct prio_queue *queue)
 {
-	void *result;
 	size_t ix, child;
 
-	if (!queue->nr)
-		return NULL;
-	if (!queue->compare)
-		return queue->array[--queue->nr].data; /* LIFO */
-
-	result = queue->array[0].data;
-	if (!--queue->nr)
-		return result;
-
-	queue->array[0] = queue->array[queue->nr];
-
 	/* Push down the one at the root */
 	for (ix = 0; ix * 2 + 1 < queue->nr; ix = child) {
 		child = ix * 2 + 1; /* left */
@@ -86,6 +74,23 @@ void *prio_queue_get(struct prio_queue *queue)
 
 		swap(queue, child, ix);
 	}
+}
+
+void *prio_queue_get(struct prio_queue *queue)
+{
+	void *result;
+
+	if (!queue->nr)
+		return NULL;
+	if (!queue->compare)
+		return queue->array[--queue->nr].data; /* LIFO */
+
+	result = queue->array[0].data;
+	if (!--queue->nr)
+		return result;
+
+	queue->array[0] = queue->array[queue->nr];
+	sift_down_root(queue);
 	return result;
 }
 
@@ -97,3 +102,17 @@ void *prio_queue_peek(struct prio_queue *queue)
 		return queue->array[queue->nr - 1].data;
 	return queue->array[0].data;
 }
+
+void prio_queue_replace(struct prio_queue *queue, void *thing)
+{
+	if (!queue->nr) {
+		prio_queue_put(queue, thing);
+	} else if (!queue->compare) {
+		queue->array[queue->nr - 1].ctr = queue->insertion_ctr++;
+		queue->array[queue->nr - 1].data = thing;
+	} else {
+		queue->array[0].ctr = queue->insertion_ctr++;
+		queue->array[0].data = thing;
+		sift_down_root(queue);
+	}
+}
diff --git a/prio-queue.h b/prio-queue.h
index 38d032636d..da7fad2f1f 100644
--- a/prio-queue.h
+++ b/prio-queue.h
@@ -52,6 +52,14 @@ void *prio_queue_get(struct prio_queue *);
  */
 void *prio_queue_peek(struct prio_queue *);
 
+/*
+ * Replace the "thing" that compares the smallest with a new "thing",
+ * like prio_queue_get()+prio_queue_put() would do, but in a more
+ * efficient way.  Does the same as prio_queue_put() if the queue is
+ * empty.
+ */
+void prio_queue_replace(struct prio_queue *queue, void *thing);
+
 void clear_prio_queue(struct prio_queue *);
 
 /* Reverse the LIFO elements */
diff --git a/t/unit-tests/u-prio-queue.c b/t/unit-tests/u-prio-queue.c
index 145e689c9c..63e58114ae 100644
--- a/t/unit-tests/u-prio-queue.c
+++ b/t/unit-tests/u-prio-queue.c
@@ -13,6 +13,7 @@ static int intcmp(const void *va, const void *vb, void *data UNUSED)
 #define STACK	 -3
 #define GET	 -4
 #define REVERSE  -5
+#define REPLACE  -6
 
 static int show(int *v)
 {
@@ -51,6 +52,15 @@ static void test_prio_queue(int *input, size_t input_size,
 		case REVERSE:
 			prio_queue_reverse(&pq);
 			break;
+		case REPLACE:
+			peek = prio_queue_peek(&pq);
+			cl_assert(i + 1 < input_size);
+			cl_assert(input[i + 1] >= 0);
+			cl_assert(j < result_size);
+			cl_assert_equal_i(result[j], show(peek));
+			j++;
+			prio_queue_replace(&pq, &input[++i]);
+			break;
 		default:
 			prio_queue_put(&pq, &input[i]);
 			break;
@@ -81,6 +91,13 @@ void test_prio_queue__empty(void)
 		   ((int []){ 1, 2, MISSING, 1, 2, MISSING }));
 }
 
+void test_prio_queue__replace(void)
+{
+	TEST_INPUT(((int []){ REPLACE, 6, 2, 4, REPLACE, 5, 7, GET,
+			      REPLACE, 1, DUMP }),
+		   ((int []){ MISSING, 2, 4, 5, 1, 6, 7 }));
+}
+
 void test_prio_queue__stack(void)
 {
 	TEST_INPUT(((int []){ STACK, 8, 1, 5, 4, 6, 2, 3, DUMP }),
@@ -92,3 +109,9 @@ void test_prio_queue__reverse_stack(void)
 	TEST_INPUT(((int []){ STACK, 1, 2, 3, 4, 5, 6, REVERSE, DUMP }),
 		   ((int []){ 1, 2, 3, 4, 5, 6 }));
 }
+
+void test_prio_queue__replace_stack(void)
+{
+	TEST_INPUT(((int []){ STACK, 8, 1, 5, REPLACE, 4, 6, 2, 3, DUMP }),
+		   ((int []){ 5, 3, 2, 6, 4, 1, 8 }));
+}