diff --git a/src/dexorder/order/orderstate.py b/src/dexorder/order/orderstate.py
index 9739131..fc61d38 100644
--- a/src/dexorder/order/orderstate.py
+++ b/src/dexorder/order/orderstate.py
@@ -106,6 +106,7 @@ class Order:
         # flattenings of various static data
         self.order = self.status.order
         self.amount = self.status.order.amount
+        self.min_fill_amount = self.status.order.minFillAmount
         self.amount_is_input = self.status.order.amountIsInput
         self.tranche_amounts = [t.fraction_of(self.amount) for t in self.order.tranches]
         Order.instances[self.key] = self
diff --git a/src/dexorder/order/triggers.py b/src/dexorder/order/triggers.py
index b31e560..d58b109 100644
--- a/src/dexorder/order/triggers.py
+++ b/src/dexorder/order/triggers.py
@@ -99,7 +99,7 @@ class TrancheTrigger:
         self.pool_price_multiplier = None
 
         # compute status and set relevant triggers
-        if tranche_remaining <= 0:
+        if tranche_remaining == 0 or tranche_remaining < self.order.min_fill_amount: # min_fill_amount could be 0 (disabled) so we also check for the 0 case separately
             self.status = TrancheStatus.Filled
             return
         timestamp = current_block.get().timestamp
@@ -164,7 +164,7 @@ class TrancheTrigger:
 
     def fill(self, _amount_in, _amount_out ):
         remaining = self.order.tranche_remaining(self.tk.tranche_index)
-        filled = remaining <= 0
+        filled = remaining == 0 or remaining < self.order.min_fill_amount
         if filled:
             log.debug(f'tranche filled {self.tk}')
             self.status = TrancheStatus.Filled