diff --git a/src/lineagetree/_basics/_navigation.py b/src/lineagetree/_basics/_navigation.py
index 9a86ea2..7c23a94 100644
--- a/src/lineagetree/_basics/_navigation.py
+++ b/src/lineagetree/_basics/_navigation.py
@@ -360,23 +360,20 @@ def nodes_at_t(
     list of int
         list of ids of the nodes at time `t` spawned by `r`
     """
-    if not r and r != 0:
-        r = {root for root in lT.roots if lT.time[root] <= t}
+    if r is None:
+        return lT.time_nodes.get(t, [])
     if isinstance(r, int):
         r = [r]
     if t is None:
         t = lT.t_e
     to_do = list(r)
     final_nodes = []
-    while len(to_do) > 0:
+    while 0 < len(to_do):
         curr = to_do.pop()
-        for _next in lT._successor[curr]:
-            if lT._time[_next] < t:
-                to_do.append(_next)
-            elif lT._time[_next] == t:
-                final_nodes.append(_next)
-    if not final_nodes:
-        return list(r)
+        if lT._time[curr] == t:
+            final_nodes.append(curr)
+        elif lT._time[curr] < t:
+            to_do.extend(lT.successor[curr])
     return final_nodes