diff --git a/inconspiquous/dialects/prob.py b/inconspiquous/dialects/prob.py
index f144775..4ffe6ff 100644
--- a/inconspiquous/dialects/prob.py
+++ b/inconspiquous/dialects/prob.py
@@ -121,7 +121,7 @@ class FinSuppOp(IRDLOperation):
     def __init__(
         self,
         probabilities: Sequence[float] | DenseArrayBase,
-        default_value: SSAValue,
+        default_value: SSAValue | Operation,
         *ins: SSAValue | Operation,
         attr_dict: dict[str, Attribute] | None = None,
     ):
diff --git a/inconspiquous/transforms/__init__.py b/inconspiquous/transforms/__init__.py
index c8de6bb..c9d0139 100644
--- a/inconspiquous/transforms/__init__.py
+++ b/inconspiquous/transforms/__init__.py
@@ -41,6 +41,11 @@ def get_lower_dyn_gate_to_scf():
 
         return lower_dyn_gate_to_scf.LowerDynGateToScf
 
+    def get_lower_to_fin_supp():
+        from inconspiquous.transforms import lower_to_fin_supp
+
+        return lower_to_fin_supp.LowerToFinSupp
+
     def get_lower_xs_to_select():
         from inconspiquous.transforms.xs import lower
 
@@ -74,6 +79,7 @@ def get_xs_select():
         "cse": get_cse,
         "dce": get_dce,
         "lower-dyn-gate-to-scf": get_lower_dyn_gate_to_scf,
+        "lower-to-fin-supp": get_lower_to_fin_supp,
         "lower-xs-to-select": get_lower_xs_to_select,
         "merge-xs": get_merge_xs,
         "mlir-opt": get_mlir_opt,
diff --git a/inconspiquous/transforms/lower_to_fin_supp.py b/inconspiquous/transforms/lower_to_fin_supp.py
new file mode 100644
index 0000000..ee53114
--- /dev/null
+++ b/inconspiquous/transforms/lower_to_fin_supp.py
@@ -0,0 +1,65 @@
+from xdsl.context import MLContext
+from xdsl.dialects import builtin
+from xdsl.dialects.builtin import BoolAttr
+from xdsl.ir import Operation, dataclass
+from xdsl.parser import IntegerType
+from xdsl.pattern_rewriter import (
+    GreedyRewritePatternApplier,
+    PatternRewriteWalker,
+    PatternRewriter,
+    RewritePattern,
+    op_type_rewrite_pattern,
+)
+from xdsl.dialects import arith
+from xdsl.passes import ModulePass
+from inconspiquous.dialects.prob import BernoulliOp, FinSuppOp, UniformOp
+
+
+class LowerBernoulli(RewritePattern):
+    @op_type_rewrite_pattern
+    def match_and_rewrite(self, op: BernoulliOp, rewriter: PatternRewriter):
+        zero = arith.Constant(BoolAttr.from_bool(False))
+        one = arith.Constant(BoolAttr.from_bool(True))
+        rewriter.replace_matched_op(
+            (zero, one, FinSuppOp((op.prob.value.data,), zero, one))
+        )
+
+
+@dataclass(frozen=True)
+class LowerUniform(RewritePattern):
+    max_size: int
+
+    @op_type_rewrite_pattern
+    def match_and_rewrite(self, op: UniformOp, rewriter: PatternRewriter):
+        ty = op.out.type
+        if not isinstance(ty, IntegerType):
+            return
+
+        if ty.bitwidth > self.max_size:
+            return
+
+        zero = arith.Constant.from_int_and_width(0, ty.bitwidth)
+        ops: list[Operation] = []
+        for i in range(1, 2**ty.bitwidth):
+            ops.append(arith.Constant.from_int_and_width(i, ty.bitwidth))
+
+        fin_supp = FinSuppOp(
+            tuple(1.0 / (2**ty.bitwidth) for _ in range(1, 2**ty.bitwidth)), zero, *ops
+        )
+
+        ops.append(zero)
+        ops.append(fin_supp)
+
+        rewriter.replace_matched_op(ops)
+
+
+@dataclass(frozen=True)
+class LowerToFinSupp(ModulePass):
+    max_size: int
+
+    name = "lower-to-fin-supp"
+
+    def apply(self, ctx: MLContext, op: builtin.ModuleOp) -> None:
+        PatternRewriteWalker(
+            GreedyRewritePatternApplier([LowerBernoulli(), LowerUniform(self.max_size)])
+        ).rewrite_op(op)
diff --git a/tests/filecheck/transforms/lower_to_fin_supp.mlir b/tests/filecheck/transforms/lower_to_fin_supp.mlir
new file mode 100644
index 0000000..1d66626
--- /dev/null
+++ b/tests/filecheck/transforms/lower_to_fin_supp.mlir
@@ -0,0 +1,21 @@
+// RUN: quopt -p lower-to-fin-supp{max_size=2} %s | filecheck %s
+
+// CHECK:    %0 = arith.constant false
+// CHECK-NEXT:    %1 = arith.constant true
+// CHECK-NEXT:    %2 = prob.fin_supp [ 0.1 of %1, else %0 ] : i1
+%0 = prob.bernoulli 0.1 : f64
+
+// CHECK-NEXT:    %3 = arith.constant true
+// CHECK-NEXT:    %4 = arith.constant false
+// CHECK-NEXT:    %5 = prob.fin_supp [ 0.5 of %3, else %4 ] : i1
+%1 = prob.uniform : i1
+
+// CHECK-NEXT:    %6 = arith.constant 1 : i2
+// CHECK-NEXT:    %7 = arith.constant 2 : i2
+// CHECK-NEXT:    %8 = arith.constant 3 : i2
+// CHECK-NEXT:    %9 = arith.constant 0 : i2
+// CHECK-NEXT:    %10 = prob.fin_supp [ 0.25 of %6, 0.25 of %7, 0.25 of %8, else %9 ] : i2
+%2 = prob.uniform : i2
+
+// CHECK-NEXT:    %11 = prob.uniform : i3
+%3 = prob.uniform : i3