diff --git a/inconspiquous/transforms/randomized_comp.py b/inconspiquous/transforms/randomized_comp.py
index 4c1d76e..ee071f4 100644
--- a/inconspiquous/transforms/randomized_comp.py
+++ b/inconspiquous/transforms/randomized_comp.py
@@ -261,6 +261,8 @@ class RandomizedComp(ModulePass):
 
     def apply(self, ctx: MLContext, op: builtin.ModuleOp) -> None:
         PatternRewriteWalker(
-            GreedyRewritePatternApplier([PadTGate(), PadHadamardGate(), PadCNotGate()]),
+            GreedyRewritePatternApplier(
+                [PadTGate(), PadTDaggerGate(), PadHadamardGate(), PadCNotGate()]
+            ),
             apply_recursively=False,  # Do not reapply
         ).rewrite_module(op)
diff --git a/tests/filecheck/transforms/randomized_compilation.mlir b/tests/filecheck/transforms/randomized_compilation.mlir
new file mode 100644
index 0000000..2188819
--- /dev/null
+++ b/tests/filecheck/transforms/randomized_compilation.mlir
@@ -0,0 +1,101 @@
+// RUN: quopt %s -p randomized-comp | filecheck %s
+
+// CHECK:      func.func @t_gate(%q : !qubit.bit) -> !qubit.bit {
+// CHECK-NEXT:   %0 = prob.uniform : i1
+// CHECK-NEXT:   %1 = prob.uniform : i1
+// CHECK-NEXT:   %2 = gate.constant #gate.id
+// CHECK-NEXT:   %3 = gate.constant #gate.x
+// CHECK-NEXT:   %4 = gate.constant #gate.z
+// CHECK-NEXT:   %5 = gate.constant #gate.s
+// CHECK-NEXT:   %6 = arith.select %0, %3, %2 : !gate.type<1>
+// CHECK-NEXT:   %7 = qssa.dyn_gate<%6> %q : !qubit.bit
+// CHECK-NEXT:   %8 = arith.select %1, %4, %2 : !gate.type<1>
+// CHECK-NEXT:   %9 = qssa.dyn_gate<%8> %7 : !qubit.bit
+// CHECK-NEXT:   %10 = qssa.gate<#gate.t> %9
+// CHECK-NEXT:   %11 = arith.select %1, %4, %2 : !gate.type<1>
+// CHECK-NEXT:   %12 = qssa.dyn_gate<%11> %10 : !qubit.bit
+// CHECK-NEXT:   %13 = qssa.dyn_gate<%6> %12 : !qubit.bit
+// CHECK-NEXT:   %14 = arith.select %0, %5, %2 : !gate.type<1>
+// CHECK-NEXT:   %q_1 = qssa.dyn_gate<%14> %13 : !qubit.bit
+// CHECK-NEXT:   func.return %q_1 : !qubit.bit
+// CHECK-NEXT: }
+func.func @t_gate(%q: !qubit.bit) -> !qubit.bit {
+  %q_1 = qssa.gate<#gate.t> %q
+  func.return %q_1 : !qubit.bit
+}
+
+// CHECK:     func.func @t_dagger_gate(%q : !qubit.bit) -> !qubit.bit {
+// CHECK-NEXT:   %0 = prob.uniform : i1
+// CHECK-NEXT:   %1 = prob.uniform : i1
+// CHECK-NEXT:   %2 = gate.constant #gate.id
+// CHECK-NEXT:   %3 = gate.constant #gate.x
+// CHECK-NEXT:   %4 = gate.constant #gate.z
+// CHECK-NEXT:   %5 = gate.constant #gate.s_dagger
+// CHECK-NEXT:   %6 = arith.select %0, %3, %2 : !gate.type<1>
+// CHECK-NEXT:   %7 = qssa.dyn_gate<%6> %q : !qubit.bit
+// CHECK-NEXT:   %8 = arith.select %1, %4, %2 : !gate.type<1>
+// CHECK-NEXT:   %9 = qssa.dyn_gate<%8> %7 : !qubit.bit
+// CHECK-NEXT:   %10 = qssa.gate<#gate.t_dagger> %9
+// CHECK-NEXT:   %11 = arith.select %1, %4, %2 : !gate.type<1>
+// CHECK-NEXT:   %12 = qssa.dyn_gate<%11> %10 : !qubit.bit
+// CHECK-NEXT:   %13 = qssa.dyn_gate<%6> %12 : !qubit.bit
+// CHECK-NEXT:   %14 = arith.select %0, %5, %2 : !gate.type<1>
+// CHECK-NEXT:   %q_1 = qssa.dyn_gate<%14> %13 : !qubit.bit
+// CHECK-NEXT:   func.return %q_1 : !qubit.bit
+// CHECK-NEXT: }
+func.func @t_dagger_gate(%q: !qubit.bit) -> !qubit.bit {
+  %q_1 = qssa.gate<#gate.t_dagger> %q
+  func.return %q_1 : !qubit.bit
+}
+
+// CHECK:      func.func @h_gate(%q : !qubit.bit) -> !qubit.bit {
+// CHECK-NEXT:   %0 = prob.uniform : i1
+// CHECK-NEXT:   %1 = prob.uniform : i1
+// CHECK-NEXT:   %2 = gate.constant #gate.id
+// CHECK-NEXT:   %3 = gate.constant #gate.x
+// CHECK-NEXT:   %4 = gate.constant #gate.z
+// CHECK-NEXT:   %5 = arith.select %0, %3, %2 : !gate.type<1>
+// CHECK-NEXT:   %6 = qssa.dyn_gate<%5> %q : !qubit.bit
+// CHECK-NEXT:   %7 = arith.select %1, %4, %2 : !gate.type<1>
+// CHECK-NEXT:   %8 = qssa.dyn_gate<%7> %6 : !qubit.bit
+// CHECK-NEXT:   %9 = qssa.gate<#gate.h> %8
+// CHECK-NEXT:   %10 = arith.select %1, %3, %2 : !gate.type<1>
+// CHECK-NEXT:   %11 = qssa.dyn_gate<%10> %9 : !qubit.bit
+// CHECK-NEXT:   %12 = arith.select %0, %4, %2 : !gate.type<1>
+// CHECK-NEXT:   %q_1 = qssa.dyn_gate<%12> %11 : !qubit.bit
+// CHECK-NEXT:   func.return %q_1 : !qubit.bit
+// CHECK-NEXT: }
+func.func @h_gate(%q: !qubit.bit) -> !qubit.bit {
+  %q_1 = qssa.gate<#gate.h> %q
+  func.return %q_1 : !qubit.bit
+}
+
+// CHECK:      func.func @cnot_gate(%q1 : !qubit.bit, %q2 : !qubit.bit) -> (!qubit.bit, !qubit.bit) {
+// CHECK-NEXT:   %0 = prob.uniform : i1
+// CHECK-NEXT:   %1 = prob.uniform : i1
+// CHECK-NEXT:   %2 = prob.uniform : i1
+// CHECK-NEXT:   %3 = prob.uniform : i1
+// CHECK-NEXT:   %4 = gate.constant #gate.id
+// CHECK-NEXT:   %5 = gate.constant #gate.x
+// CHECK-NEXT:   %6 = gate.constant #gate.z
+// CHECK-NEXT:   %7 = arith.select %0, %5, %4 : !gate.type<1>
+// CHECK-NEXT:   %8 = arith.select %1, %5, %4 : !gate.type<1>
+// CHECK-NEXT:   %9 = arith.select %2, %6, %4 : !gate.type<1>
+// CHECK-NEXT:   %10 = arith.select %3, %6, %4 : !gate.type<1>
+// CHECK-NEXT:   %11 = qssa.dyn_gate<%7> %q1 : !qubit.bit
+// CHECK-NEXT:   %12 = qssa.dyn_gate<%9> %11 : !qubit.bit
+// CHECK-NEXT:   %13 = qssa.dyn_gate<%8> %q2 : !qubit.bit
+// CHECK-NEXT:   %14 = qssa.dyn_gate<%10> %13 : !qubit.bit
+// CHECK-NEXT:   %15, %16 = qssa.gate<#gate.cnot> %12, %14
+// CHECK-NEXT:   %17 = qssa.dyn_gate<%9> %15 : !qubit.bit
+// CHECK-NEXT:   %18 = qssa.dyn_gate<%10> %17 : !qubit.bit
+// CHECK-NEXT:   %19 = qssa.dyn_gate<%10> %16 : !qubit.bit
+// CHECK-NEXT:   %20 = qssa.dyn_gate<%7> %19 : !qubit.bit
+// CHECK-NEXT:   %q1_1 = qssa.dyn_gate<%7> %18 : !qubit.bit
+// CHECK-NEXT:   %q2_1 = qssa.dyn_gate<%8> %20 : !qubit.bit
+// CHECK-NEXT:   func.return %q1_1, %q2_1 : !qubit.bit, !qubit.bit
+// CHECK-NEXT: }
+func.func @cnot_gate(%q1: !qubit.bit, %q2: !qubit.bit) -> (!qubit.bit, !qubit.bit) {
+  %q1_1, %q2_1 = qssa.gate<#gate.cnot> %q1, %q2
+  func.return %q1_1, %q2_1 : !qubit.bit, !qubit.bit
+}