diff --git a/Modules/_sqlite/statement.c b/Modules/_sqlite/statement.c
index 55923e7..dee811f 100644
--- a/Modules/_sqlite/statement.c
+++ b/Modules/_sqlite/statement.c
@@ -237,7 +237,11 @@
          */
         #ifdef SQLITE_VERSION_NUMBER
         #if SQLITE_VERSION_NUMBER >= 3002002
-        (void)sqlite3_transfer_bindings(self->st, new_st);
+        /* The check for the number of parameters is necessary to not trigger a
+         * bug in certain SQLite versions (experienced in 3.2.8 and 3.3.4). */
+        if (sqlite3_bind_parameter_count(self->st) > 0) {
+            (void)sqlite3_transfer_bindings(self->st, new_st);
+        }
         #endif
         #else
         statement_bind_parameters(self, params);
diff --git a/Modules/_sqlite/util.c b/Modules/_sqlite/util.c
index f5a7233..cbaee92 100644
--- a/Modules/_sqlite/util.c
+++ b/Modules/_sqlite/util.c
@@ -29,9 +29,15 @@
 {
     int rc;
 
-    Py_BEGIN_ALLOW_THREADS
-    rc = sqlite3_step(statement);
-    Py_END_ALLOW_THREADS
+    if (statement == NULL) {
+        /* this is a workaround for SQLite 3.5 and later. it now apparently
+         * returns NULL for "no-operation" statements */
+        rc = SQLITE_OK;
+    } else {
+        Py_BEGIN_ALLOW_THREADS
+        rc = sqlite3_step(statement);
+        Py_END_ALLOW_THREADS
+    }
 
     return rc;
 }