diff --git a/include/circt/Dialect/RTG/Reductions/RTGReductions.h b/include/circt/Dialect/RTG/Reductions/RTGReductions.h
new file mode 100644
index 000000000000..00e96396ae09
--- /dev/null
+++ b/include/circt/Dialect/RTG/Reductions/RTGReductions.h
@@ -0,0 +1,29 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef CIRCT_DIALECT_RTG_REDUCTIONS_RTGREDUCTIONS_H
+#define CIRCT_DIALECT_RTG_REDUCTIONS_RTGREDUCTIONS_H
+
+#include "circt/Reduce/Reduction.h"
+
+namespace circt {
+namespace rtg {
+
+/// A dialect interface to provide reduction patterns to a reducer tool.
+struct RTGReducePatternDialectInterface : public ReducePatternDialectInterface {
+  using ReducePatternDialectInterface::ReducePatternDialectInterface;
+  void populateReducePatterns(circt::ReducePatternSet &patterns) const override;
+};
+
+/// Register the RTG Reduction pattern dialect interface to the given registry.
+void registerReducePatternDialectInterface(mlir::DialectRegistry &registry);
+
+} // namespace rtg
+} // namespace circt
+
+#endif // CIRCT_DIALECT_RTG_REDUCTIONS_RTGREDUCTIONS_H
diff --git a/lib/Dialect/RTG/CMakeLists.txt b/lib/Dialect/RTG/CMakeLists.txt
index 9f57627c321f..e55dac655bc9 100644
--- a/lib/Dialect/RTG/CMakeLists.txt
+++ b/lib/Dialect/RTG/CMakeLists.txt
@@ -1,2 +1,3 @@
 add_subdirectory(IR)
+add_subdirectory(Reductions)
 add_subdirectory(Transforms)
diff --git a/lib/Dialect/RTG/Reductions/CMakeLists.txt b/lib/Dialect/RTG/Reductions/CMakeLists.txt
new file mode 100644
index 000000000000..89b630ee18bb
--- /dev/null
+++ b/lib/Dialect/RTG/Reductions/CMakeLists.txt
@@ -0,0 +1,8 @@
+add_circt_library(CIRCTRTGReductions
+  RTGReductions.cpp
+
+  LINK_LIBS PUBLIC
+  CIRCTReduceLib
+  CIRCTRTGDialect
+  MLIRIR
+)
diff --git a/lib/Dialect/RTG/Reductions/RTGReductions.cpp b/lib/Dialect/RTG/Reductions/RTGReductions.cpp
new file mode 100644
index 000000000000..1b01363ce766
--- /dev/null
+++ b/lib/Dialect/RTG/Reductions/RTGReductions.cpp
@@ -0,0 +1,62 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "circt/Dialect/RTG/Reductions/RTGReductions.h"
+#include "circt/Dialect/RTG/IR/RTGOps.h"
+
+using namespace mlir;
+using namespace circt;
+using namespace rtg;
+
+//===----------------------------------------------------------------------===//
+// Reduction patterns
+//===----------------------------------------------------------------------===//
+
+namespace {
+
+/// Replace virtual registers with a constant register.
+struct VirtualRegisterConstantifier : public OpReduction<VirtualRegisterOp> {
+  LogicalResult rewrite(VirtualRegisterOp op) override {
+    if (op.getAllowedRegs().getAllowedRegs().empty())
+      return failure();
+
+    OpBuilder builder(op);
+    auto constReg = ConstantOp::create(builder, op.getLoc(),
+                                       op.getAllowedRegs().getAllowedRegs()[0]);
+    op.getResult().replaceAllUsesWith(constReg);
+    op.erase();
+    return success();
+  }
+
+  std::string getName() const override {
+    return "rtg-virtual-register-constantifier";
+  }
+};
+
+} // namespace
+
+//===----------------------------------------------------------------------===//
+// Reduction Registration
+//===----------------------------------------------------------------------===//
+
+void RTGReducePatternDialectInterface::populateReducePatterns(
+    circt::ReducePatternSet &patterns) const {
+  // Gather a list of reduction patterns that we should try. Ideally these are
+  // assigned reasonable benefit indicators (higher benefit patterns are
+  // prioritized). For example, things that can knock out entire modules while
+  // being cheap should be tried first (and thus have higher benefit), before
+  // trying to tweak operands of individual arithmetic ops.
+  patterns.add<VirtualRegisterConstantifier, 2>();
+}
+
+void rtg::registerReducePatternDialectInterface(
+    mlir::DialectRegistry &registry) {
+  registry.addExtension(+[](MLIRContext *ctx, RTGDialect *dialect) {
+    dialect->addInterfaces<RTGReducePatternDialectInterface>();
+  });
+}
diff --git a/test/Dialect/RTG/Reduction/virtual-register-constantifier.mlir b/test/Dialect/RTG/Reduction/virtual-register-constantifier.mlir
new file mode 100644
index 000000000000..590bd0058cd7
--- /dev/null
+++ b/test/Dialect/RTG/Reduction/virtual-register-constantifier.mlir
@@ -0,0 +1,11 @@
+// UNSUPPORTED: system-windows
+//   See https://github.com/llvm/circt/issues/4129
+// RUN: circt-reduce %s --test /usr/bin/env --test-arg grep --test-arg -q --test-arg "rtg.test @test" --keep-best=0 --include rtg-virtual-register-constantifier | FileCheck %s
+
+// CHECK-LABEL: rtg.test @test
+rtg.test @test() {
+  // CHECK-NEXT: [[V0:%.+]] = rtg.constant #rtgtest.t0 : !rtgtest.ireg
+  // CHECK-NEXT: rtgtest.rv32i.add [[V0]], [[V0]], [[V0]]
+  %reg = rtg.virtual_reg [#rtgtest.t0, #rtgtest.t1, #rtgtest.t2]
+  rtgtest.rv32i.add %reg, %reg, %reg
+}
diff --git a/tools/circt-reduce/CMakeLists.txt b/tools/circt-reduce/CMakeLists.txt
index 1d503c4aa74a..be198fa05f7d 100644
--- a/tools/circt-reduce/CMakeLists.txt
+++ b/tools/circt-reduce/CMakeLists.txt
@@ -13,6 +13,7 @@ set(LIBS
   CIRCTEmitReductions
   CIRCTHWReductions
   CIRCTFIRRTLReductions
+  CIRCTRTGReductions
   CIRCTReduceLib
   MLIRIR
   MLIRBytecodeWriter
diff --git a/tools/circt-reduce/circt-reduce.cpp b/tools/circt-reduce/circt-reduce.cpp
index 40696d1367d4..69ef52888b20 100644
--- a/tools/circt-reduce/circt-reduce.cpp
+++ b/tools/circt-reduce/circt-reduce.cpp
@@ -16,6 +16,7 @@
 #include "circt/Dialect/FIRRTL/FIRRTLReductions.h"
 #include "circt/Dialect/HW/HWDialect.h"
 #include "circt/Dialect/HW/HWReductions.h"
+#include "circt/Dialect/RTG/Reductions/RTGReductions.h"
 #include "circt/InitAllDialects.h"
 #include "circt/Reduce/GenericReductions.h"
 #include "circt/Reduce/Tester.h"
@@ -532,6 +533,7 @@ int main(int argc, char **argv) {
   emit::registerReducePatternDialectInterface(registry);
   firrtl::registerReducePatternDialectInterface(registry);
   hw::registerReducePatternDialectInterface(registry);
+  rtg::registerReducePatternDialectInterface(registry);
 
   // Set up dialect plugin loading callback
   dialectPlugins.setCallback([&](const std::string &pluginPath) {