diff --git a/src/compose/table.c b/src/compose/table.c
index 078b719a0..f58332686 100644
--- a/src/compose/table.c
+++ b/src/compose/table.c
@@ -314,28 +314,47 @@ xkb_compose_table_iterator_current(struct xkb_compose_table_iterator *iter)
 XKB_EXPORT struct xkb_compose_table_entry *
 xkb_compose_table_iterator_next(struct xkb_compose_table_iterator *iter)
 {
+    /*
+     * This function takes the following recursive traversal function,
+     * and makes it non-recursive and resumable. The iter->cursors stack
+     * is analogous to the call stack, and cursor->direction to the
+     * instruction pointer of a stack frame.
+     *
+     *    traverse(xkb_keysym_t *sequence, size_t sequence_length, uint16_t p) {
+     *        if (!p) return
+     *        // cursor->direction == NODE_LEFT
+     *        node = &darray_item(table->nodes, p)
+     *        traverse(sequence, sequence_length, node->lokid)
+     *        // cursor->direction == NODE_DOWN
+     *        sequence[sequence_length++] = node->keysym
+     *        if (node->is_leaf)
+     *            emit(sequence, sequence_length, node->leaf.keysym, table->utf[node->leaf.utf8])
+     *        else
+     *            traverse(sequence, sequence_length, node->internal.eqkid)
+     *        sequence_length--
+     *        // cursor->direction == NODE_RIGHT
+     *        traverse(sequence, sequence_length, node->hikid)
+     *        // cursor->direction == NODE_UP
+     *    }
+     */
+
     struct xkb_compose_table_iterator_cursor *cursor;
-    struct xkb_compose_table_iterator_cursor new_cursor;
     const struct compose_node *node;
 
-    cursor = &darray_item(iter->cursors, darray_size(iter->cursors) - 1);
-    new_cursor.direction = NODE_LEFT;
-
-    while (cursor->direction < NODE_UP) {
+    while (!darray_empty(iter->cursors)) {
+        cursor = &darray_item(iter->cursors, darray_size(iter->cursors) - 1);
         node = &darray_item(iter->table->nodes, cursor->node_offset);
 
-        if (cursor->direction == NODE_LEFT) {
-            /* Left node */
+        switch (cursor->direction) {
+        case NODE_LEFT:
             cursor->direction = NODE_DOWN;
             if (node->lokid) {
-                new_cursor.node_offset = node->lokid;
+                struct xkb_compose_table_iterator_cursor new_cursor = {node->lokid, NODE_LEFT};
                 darray_append(iter->cursors, new_cursor);
-                cursor = &darray_item(iter->cursors, darray_size(iter->cursors) - 1);
-                continue;
             }
-        }
-        if (cursor->direction == NODE_DOWN) {
-            /* Down node */
+            break;
+
+        case NODE_DOWN:
             cursor->direction = NODE_RIGHT;
             assert (iter->entry.sequence_length <= MAX_LHS_LEN);
             iter->entry.sequence[iter->entry.sequence_length] = node->keysym;
@@ -345,32 +364,25 @@ xkb_compose_table_iterator_next(struct xkb_compose_table_iterator *iter)
                 iter->entry.utf8 = &darray_item(iter->table->utf8, node->leaf.utf8);
                 return &iter->entry;
             } else {
-                new_cursor.node_offset = node->internal.eqkid;
+                struct xkb_compose_table_iterator_cursor new_cursor = {node->internal.eqkid, NODE_LEFT};
                 darray_append(iter->cursors, new_cursor);
-                cursor = &darray_item(iter->cursors, darray_size(iter->cursors) - 1);
-                continue;
             }
-        }
-        cursor->direction = NODE_UP;
-        iter->entry.sequence_length--;
-        if (node->hikid) {
-            /* Right node */
-            new_cursor.node_offset = node->hikid;
-            darray_append(iter->cursors, new_cursor);
-            cursor = &darray_item(iter->cursors, darray_size(iter->cursors) - 1);
-            continue;
-        } else {
-            /* Look for next node in parents */
-            while (darray_size(iter->cursors) > 1) {
-                darray_remove_last(iter->cursors);
-                cursor = &darray_item(iter->cursors, darray_size(iter->cursors) - 1);
-                if (cursor->direction < NODE_UP) {
-                    break;
-                }
+            break;
+
+        case NODE_RIGHT:
+            cursor->direction = NODE_UP;
+            iter->entry.sequence_length--;
+            if (node->hikid) {
+                struct xkb_compose_table_iterator_cursor new_cursor = {node->hikid, NODE_LEFT};
+                darray_append(iter->cursors, new_cursor);
             }
+            break;
+
+        case NODE_UP:
+            darray_remove_last(iter->cursors);
+            break;
         }
     }
 
     return NULL;
-
 }