diff --git a/lib/dns/qp.c b/lib/dns/qp.c
index bb212fdfba..1fd36b91ba 100644
--- a/lib/dns/qp.c
+++ b/lib/dns/qp.c
@@ -2139,12 +2139,14 @@ dns_qp_lookup(dns_qpreadable_t qpr, const dns_name_t *name,
 			 */
 			size_t to;
 			dns_qpnode_t *least = n;
+
+		least:
 			while (is_branch(least)) {
 				least = branch_twigs(qp, least);
 			}
 			foundlen = leaf_qpkey(qp, least, found);
 			to = qpkey_compare(search, searchlen, found, foundlen);
-			if (to == offset) {
+			if (to >= offset) {
 				/*
 				 * we're on the right branch, so find
 				 * the best match.
@@ -2180,9 +2182,12 @@ dns_qp_lookup(dns_qpreadable_t qpr, const dns_name_t *name,
 				 * we wanted, so iterate back to the
 				 * predecessor.
 				 */
+				iter->sp--;
 				prevleaf(iter);
-				n = iter->stack[iter->sp--];
-			} else {
+				n = iter->stack[iter->sp];
+				least = n;
+				goto least;
+			} else if (is_branch(n)) {
 				/*
 				 * every leaf is less than the one we
 				 * wanted, so get the highest.
diff --git a/tests/dns/qp_test.c b/tests/dns/qp_test.c
index 44f8ded9b2..3889de5eda 100644
--- a/tests/dns/qp_test.c
+++ b/tests/dns/qp_test.c
@@ -635,11 +635,12 @@ check_predecessors(dns_qp_t *qp, struct check_predecessors check[]) {
 
 ISC_RUN_TEST_IMPL(predecessors) {
 	dns_qp_t *qp = NULL;
-	const char insert[][16] = { "a.",	  "b.",		"c.b.a.",
-				    "e.d.c.b.a.", "c.b.b.",	"c.d.",
-				    "a.b.c.d.",	  "a.b.c.d.e.", "b.a.",
-				    "x.k.c.d.",	  "moog.",	"mook.",
-				    "moon.",	  "moops.",	"" };
+	const char insert[][16] = {
+		"a.",	  "b.",	      "c.b.a.",	  "e.d.c.b.a.",
+		"c.b.b.", "c.d.",     "a.b.c.d.", "a.b.c.d.e.",
+		"b.a.",	  "x.k.c.d.", "moog.",	  "mooker.",
+		"mooko.", "moon.",    "moops.",	  ""
+	};
 	int i = 0;
 
 	dns_qp_create(mctx, &string_methods, NULL, &qp);
@@ -669,14 +670,19 @@ ISC_RUN_TEST_IMPL(predecessors) {
 		{ "moor.", "moops.", ISC_R_NOTFOUND },
 		{ "mopbop.", "moops.", ISC_R_NOTFOUND },
 		{ "moppop.", "moops.", ISC_R_NOTFOUND },
+		{ "mopps.", "moops.", ISC_R_NOTFOUND },
 		{ "mopzop.", "moops.", ISC_R_NOTFOUND },
 		{ "mop.", "moops.", ISC_R_NOTFOUND },
 		{ "monbop.", "a.b.c.d.e.", ISC_R_NOTFOUND },
 		{ "monpop.", "a.b.c.d.e.", ISC_R_NOTFOUND },
+		{ "monps.", "a.b.c.d.e.", ISC_R_NOTFOUND },
 		{ "monzop.", "a.b.c.d.e.", ISC_R_NOTFOUND },
 		{ "mon.", "a.b.c.d.e.", ISC_R_NOTFOUND },
 		{ "moop.", "moon.", ISC_R_NOTFOUND },
 		{ "moopser.", "moops.", ISC_R_NOTFOUND },
+		{ "monky.", "a.b.c.d.e.", ISC_R_NOTFOUND },
+		{ "monkey.", "a.b.c.d.e.", ISC_R_NOTFOUND },
+		{ "monker.", "a.b.c.d.e.", ISC_R_NOTFOUND },
 		{ NULL, NULL, 0 }
 	};
 
@@ -706,14 +712,19 @@ ISC_RUN_TEST_IMPL(predecessors) {
 		{ "moor.", "moops.", DNS_R_PARTIALMATCH },
 		{ "mopbop.", "moops.", DNS_R_PARTIALMATCH },
 		{ "moppop.", "moops.", DNS_R_PARTIALMATCH },
+		{ "mopps.", "moops.", DNS_R_PARTIALMATCH },
 		{ "mopzop.", "moops.", DNS_R_PARTIALMATCH },
 		{ "mop.", "moops.", DNS_R_PARTIALMATCH },
 		{ "monbop.", "a.b.c.d.e.", DNS_R_PARTIALMATCH },
 		{ "monpop.", "a.b.c.d.e.", DNS_R_PARTIALMATCH },
+		{ "monps.", "a.b.c.d.e.", DNS_R_PARTIALMATCH },
 		{ "monzop.", "a.b.c.d.e.", DNS_R_PARTIALMATCH },
 		{ "mon.", "a.b.c.d.e.", DNS_R_PARTIALMATCH },
 		{ "moop.", "moon.", DNS_R_PARTIALMATCH },
 		{ "moopser.", "moops.", DNS_R_PARTIALMATCH },
+		{ "monky.", "a.b.c.d.e.", DNS_R_PARTIALMATCH },
+		{ "monkey.", "a.b.c.d.e.", DNS_R_PARTIALMATCH },
+		{ "monker.", "a.b.c.d.e.", DNS_R_PARTIALMATCH },
 		{ NULL, NULL, 0 }
 	};