diff --git a/direct/src/interval/Interval.py b/direct/src/interval/Interval.py
index 6ea262398d..a22b72170b 100644
--- a/direct/src/interval/Interval.py
+++ b/direct/src/interval/Interval.py
@@ -62,8 +62,19 @@ class Interval(DirectObject):
         state = self.getState()
         if state == CInterval.SInitial:
             self.privInitialize(t)
+            if self.isPlaying():
+                self.setupResume()
         elif state == CInterval.SFinal:
             self.privReverseInitialize(t)
+            if self.isPlaying():
+                self.setupResume()
+        elif state == CInterval.SStarted:
+            # Support modifying t while the interval is playing.  We
+            # assume is_playing() will be true in this state.
+            assert(self.isPlaying())
+            self.privInterrupt()
+            self.privStep(t)
+            self.setupResume()
         else:
             self.privStep(t)
         self.privPostEvent()
diff --git a/direct/src/interval/cInterval.cxx b/direct/src/interval/cInterval.cxx
index c0884774ea..12bf5f73a8 100644
--- a/direct/src/interval/cInterval.cxx
+++ b/direct/src/interval/cInterval.cxx
@@ -70,10 +70,25 @@ set_t(double t) {
   switch (get_state()) {
   case S_initial:
     priv_initialize(t);
+    if (is_playing()) {
+      setup_resume();
+    }
     break;
 
   case S_final:
     priv_reverse_initialize(t);
+    if (is_playing()) {
+      setup_resume();
+    }
+    break;
+
+  case S_started:
+    // Support modifying t while the interval is playing.  We assume
+    // is_playing() will be true in this state.
+    nassertv(is_playing());
+    priv_interrupt();
+    priv_step(t);
+    setup_resume();
     break;
 
   default: