diff --git a/CHANGES b/CHANGES
index 8e6d993723..79d4b4e664 100644
--- a/CHANGES
+++ b/CHANGES
@@ -1,3 +1,6 @@
+5073.	[bug]		Destroy a task first when destroying rpzs and catzs.
+			[GL #84]
+
 5072.	[bug]		Add unit tests for isc_buffer_copyregion() and fix its
 			behavior for auto-reallocated buffers. [GL #644]
 
diff --git a/lib/dns/catz.c b/lib/dns/catz.c
index 848e42a2b5..ca42a55f7d 100644
--- a/lib/dns/catz.c
+++ b/lib/dns/catz.c
@@ -795,7 +795,7 @@ dns_catz_catzs_detach(dns_catz_zones_t **catzsp) {
 	*catzsp = NULL;
 
 	if (isc_refcount_decrement(&catzs->refs) == 1) {
-		isc_refcount_destroy(&catzs->refs);
+		isc_task_destroy(&catzs->updater);
 		DESTROYLOCK(&catzs->lock);
 		if (catzs->zones != NULL) {
 			isc_ht_iter_t *iter = NULL;
@@ -815,7 +815,7 @@ dns_catz_catzs_detach(dns_catz_zones_t **catzsp) {
 			INSIST(isc_ht_count(catzs->zones) == 0);
 			isc_ht_destroy(&catzs->zones);
 		}
-		isc_task_destroy(&catzs->updater);
+		isc_refcount_destroy(&catzs->refs);
 		isc_mem_putanddetach(&catzs->mctx, catzs, sizeof(*catzs));
 	}
 }
diff --git a/lib/dns/rpz.c b/lib/dns/rpz.c
index 38fd3bd2cd..00751923e2 100644
--- a/lib/dns/rpz.c
+++ b/lib/dns/rpz.c
@@ -2148,7 +2148,12 @@ dns_rpz_detach_rpzs(dns_rpz_zones_t **rpzsp) {
 	*rpzsp = NULL;
 
 	if (isc_refcount_decrement(&rpzs->refs) == 1) {
-		isc_refcount_destroy(&rpzs->refs);
+		/*
+		 * Destroy the task first, so that nothing runs
+		 * in the background that might race with us.
+		 */
+		isc_task_destroy(&rpzs->updater);
+
 		/*
 		 * Forget the last of view's rpz machinery after
 		 * the last reference.
@@ -2178,7 +2183,7 @@ dns_rpz_detach_rpzs(dns_rpz_zones_t **rpzsp) {
 		}
 		DESTROYLOCK(&rpzs->maint_lock);
 		isc_rwlock_destroy(&rpzs->search_lock);
-		isc_task_destroy(&rpzs->updater);
+		isc_refcount_destroy(&rpzs->refs);
 		isc_mem_putanddetach(&rpzs->mctx, rpzs, sizeof(*rpzs));
 	}
 }