diff --git a/lib/dns/qp.c b/lib/dns/qp.c
index 686c3561f5..e381b7c324 100644
--- a/lib/dns/qp.c
+++ b/lib/dns/qp.c
@@ -2152,15 +2152,42 @@ fix_iterator(dns_qpreader_t *qp, dns_qpiter_t *iter, dns_qpnode_t *start,
 			n = iter->stack[iter->sp];
 			leaf = n;
 		} else {
+			if (to <= searchlen && to <= foundlen && iter->sp > 0) {
+				/*
+				 * If we're here, search[to] >= found[to],
+				 * meaning every leaf in this set of twigs
+				 * is less than the one we wanted. It's
+				 * possible we're already positioned at
+				 * the correct predecessor, but it's not
+				 * guaranteed, so we pop up to the parent
+				 * branch, and find the greatest leaf from
+				 * there.
+				 */
+				if (!is_branch(n)) {
+					iter->stack[iter->sp--] = NULL;
+					n = iter->stack[iter->sp];
+				}
+			}
+
 			if (is_branch(n)) {
-				iter->sp--;
+				iter->stack[iter->sp--] = NULL;
 				n = greatest_leaf(qp, n, iter);
 			}
 			return (n);
 		}
 
 		foundlen = leaf_qpkey(qp, leaf, found);
-		to = qpkey_compare(search, searchlen, found, foundlen);
+
+		size_t nto = qpkey_compare(search, searchlen, found, foundlen);
+		if (nto < to) {
+			/*
+			 * We've moved to a new leaf and it differs at an
+			 * even earlier point, so no further improvement is
+			 * possible.
+			 */
+			return (leaf);
+		}
+		to = nto;
 	}
 
 	if (is_branch(n)) {
@@ -2293,8 +2320,7 @@ dns_qp_lookup(dns_qpreadable_t qpr, const dns_name_t *name,
 			 */
 			n = fix_iterator(qp, iter, n, search, searchlen, bit,
 					 offset);
-			iter->stack[iter->sp] = NULL;
-			iter->sp--;
+			iter->stack[iter->sp--] = NULL;
 		} else {
 			/*
 			 * this branch is a dead end, and the predecessor
diff --git a/tests/dns/qp_test.c b/tests/dns/qp_test.c
index 6938cb9fd8..d49fe674b3 100644
--- a/tests/dns/qp_test.c
+++ b/tests/dns/qp_test.c
@@ -765,29 +765,29 @@ ISC_RUN_TEST_IMPL(predecessors) {
  */
 ISC_RUN_TEST_IMPL(fixiterator) {
 	dns_qp_t *qp = NULL;
-	const char insert[][32] = { "dynamic.",
-				    "a.dynamic.",
-				    "aaaa.dynamic.",
-				    "cdnskey.dynamic.",
-				    "cds.dynamic.",
-				    "cname.dynamic.",
-				    "dname.dynamic.",
-				    "dnskey.dynamic.",
-				    "ds.dynamic.",
-				    "mx.dynamic.",
-				    "ns.dynamic.",
-				    "nsec.dynamic.",
-				    "private-cdnskey.dynamic.",
-				    "private-dnskey.dynamic.",
-				    "rrsig.dynamic.",
-				    "txt.dynamic.",
-				    "trailing.",
-				    "" };
+	const char insert1[][32] = { "dynamic.",
+				     "a.dynamic.",
+				     "aaaa.dynamic.",
+				     "cdnskey.dynamic.",
+				     "cds.dynamic.",
+				     "cname.dynamic.",
+				     "dname.dynamic.",
+				     "dnskey.dynamic.",
+				     "ds.dynamic.",
+				     "mx.dynamic.",
+				     "ns.dynamic.",
+				     "nsec.dynamic.",
+				     "private-cdnskey.dynamic.",
+				     "private-dnskey.dynamic.",
+				     "rrsig.dynamic.",
+				     "txt.dynamic.",
+				     "trailing.",
+				     "" };
 	int i = 0;
 
 	dns_qp_create(mctx, &string_methods, NULL, &qp);
-	while (insert[i][0] != '\0') {
-		insert_str(qp, insert[i++]);
+	while (insert1[i][0] != '\0') {
+		insert_str(qp, insert1[i++]);
 	}
 
 	static struct check_predecessors check1[] = {
@@ -800,7 +800,25 @@ ISC_RUN_TEST_IMPL(fixiterator) {
 	};
 
 	check_predecessors(qp, check1);
+	dns_qp_destroy(&qp);
 
+	const char insert2[][64] = { ".", "abb.", "abc.", "" };
+	i = 0;
+
+	dns_qp_create(mctx, &string_methods, NULL, &qp);
+	while (insert2[i][0] != '\0') {
+		insert_str(qp, insert2[i++]);
+	}
+
+	static struct check_predecessors check2[] = {
+		{ "acb.", "abc.", DNS_R_PARTIALMATCH, 0 },
+		{ "acc.", "abc.", DNS_R_PARTIALMATCH, 0 },
+		{ "abbb.", "abb.", DNS_R_PARTIALMATCH, 1 },
+		{ "aab.", ".", DNS_R_PARTIALMATCH, 2 },
+		{ NULL, NULL, 0, 0 }
+	};
+
+	check_predecessors(qp, check2);
 	dns_qp_destroy(&qp);
 }