diff --git a/src/pf1e_simulator/dice.py b/src/pf1e_simulator/dice.py
index 5e45945..f33123b 100644
--- a/src/pf1e_simulator/dice.py
+++ b/src/pf1e_simulator/dice.py
@@ -103,15 +103,13 @@ def parse_dice(text: str) -> DiceExpr:
     m = _DICE_RE.match(stripped)
     if m:
         count_str, sides_str, bonus_str = m.groups()
-        if not sides_str:
-            raise DiceParseError(text)
         count = int(count_str) if count_str else 1
         sides = int(sides_str)
         bonus = int(bonus_str) if bonus_str else 0
 
         if count == 0:
             raise DiceParseError(text)
-        if sides < 1:
+        if sides < _MIN_SIDES:
             raise DiceParseError(text)
 
         return DiceExpr(count=count, sides=sides, bonus=bonus)
diff --git a/tests/test_dice.py b/tests/test_dice.py
index 0ffe400..4bca8b6 100644
--- a/tests/test_dice.py
+++ b/tests/test_dice.py
@@ -88,6 +88,9 @@ class TestParseDiceRejected:
             "d",
             "2d0",
             "0d6",
+            "d1",
+            "1d1",
+            "2D6",
             "2d 6",
             "abc",
             "d6+",