diff --git a/passes/opt/opt_expr.cc b/passes/opt/opt_expr.cc
index 62a0ffc48..9967c7753 100644
--- a/passes/opt/opt_expr.cc
+++ b/passes/opt/opt_expr.cc
@@ -1690,7 +1690,38 @@ skip_identity:
 			else if (inA == inB)
 				ACTION_DO(ID::Y, cell->getPort(ID::A));
 		}
+		if (cell->type == ID($pow) && cell->getPort(ID::A).is_fully_const() && !cell->parameters[ID::B_SIGNED].as_bool()) {
+			SigSpec sig_a = assign_map(cell->getPort(ID::A));
+			SigSpec sig_y = assign_map(cell->getPort(ID::Y));
+			int y_size = GetSize(sig_y);
 
+			int bit_idx;
+			const auto onehot = sig_a.is_onehot(&bit_idx);
+
+			if (onehot) {
+				if (bit_idx == 1) {
+					log_debug("Replacing pow cell `%s' in module `%s' with left-shift\n", 
+							cell->name.c_str(), module->name.c_str());
+					cell->type = ID($shl);
+					cell->parameters[ID::A_WIDTH] = 1;
+					cell->setPort(ID::A, Const(State::S1, 1));
+				}
+				else {
+					log_debug("Replacing pow cell `%s' in module `%s' with multiply and left-shift\n", 
+							cell->name.c_str(), module->name.c_str());
+					cell->type = ID($mul);
+					cell->parameters[ID::A_SIGNED] = 0;
+					cell->setPort(ID::A, Const(bit_idx, cell->parameters[ID::A_WIDTH].as_int()));
+					
+					SigSpec y_wire = module->addWire(NEW_ID, y_size);
+					cell->setPort(ID::Y, y_wire);
+					
+					module->addShl(NEW_ID, Const(State::S1, 1), y_wire, sig_y);
+				}
+				did_something = true;
+				goto next_cell;
+			}
+		}
 		if (!keepdc && cell->type == ID($mul))
 		{
 			bool a_signed = cell->parameters[ID::A_SIGNED].as_bool();
diff --git a/tests/opt/opt_pow.ys b/tests/opt/opt_pow.ys
new file mode 100644
index 000000000..0fa2f88c7
--- /dev/null
+++ b/tests/opt/opt_pow.ys
@@ -0,0 +1,89 @@
+# Default power of two
+
+design -reset
+
+read_rtlil << EOT
+autoidx 3
+attribute \cells_not_processed 1
+attribute \src "<stdin>:1.1-3.10"
+module \top
+  attribute \src "<stdin>:2.17-2.20"
+  wire width 32 $add$<stdin>:2$1_Y
+  attribute \src "<stdin>:2.12-2.21"
+  wire width 32 signed $pow$<stdin>:2$2_Y
+  attribute \src "<stdin>:1.29-1.30"
+  wire width 15 input 1 \a
+  attribute \src "<stdin>:1.51-1.52"
+  wire width 32 output 2 \b
+  attribute \src "<stdin>:2.17-2.20"
+  cell $add $add$<stdin>:2$1
+    parameter \A_SIGNED 0
+    parameter \A_WIDTH 15
+    parameter \B_SIGNED 0
+    parameter \B_WIDTH 32
+    parameter \Y_WIDTH 32
+    connect \A \a
+    connect \B 2
+    connect \Y $add$<stdin>:2$1_Y
+  end
+  attribute \src "<stdin>:2.12-2.21"
+  cell $pow $pow$<stdin>:2$2
+    parameter \A_SIGNED 0
+    parameter \A_WIDTH 32
+    parameter \B_SIGNED 0
+    parameter \B_WIDTH 32
+    parameter \Y_WIDTH 32
+    connect \A 2
+   connect \B $add$<stdin>:2$1_Y
+    connect \Y $pow$<stdin>:2$2_Y
+  end
+  connect \b $pow$<stdin>:2$2_Y
+end
+EOT
+
+select -assert-count 1 t:$pow
+select -assert-none t:$shl
+opt_expr
+select -assert-none t:$pow
+select -assert-count 1 t:$shl
+
+read_verilog << EOT
+module ref(input wire [14:0] a, output wire [31:0] b);
+assign b = 1 << (a+2);
+endmodule
+EOT
+
+equiv_make top ref equiv
+select -assert-any -module equiv t:$equiv
+equiv_induct
+equiv_status -assert
+
+# Other power of 2 value
+
+design -reset
+
+read_verilog <<EOT
+module top(input wire [14:0] a, output wire [31:0] b);
+assign b = 128**(a+2);
+endmodule
+EOT
+
+# Check the cell counts have changed correctly
+select -assert-count 1 t:$pow
+select -assert-none t:$shl
+select -assert-none t:$mul
+opt_expr
+select -assert-none t:$pow
+select -assert-count 1 t:$shl
+select -assert-count 1 t:$mul
+
+read_verilog <<EOT
+module ref(input wire [14:0] a, output wire [31:0] b);
+assign b = 1 << (7 * (a+2));
+endmodule
+EOT
+
+equiv_make top ref equiv
+select -assert-any -module equiv t:$equiv
+equiv_induct
+equiv_status -assert