diff --git a/passes/opt/Makefile.inc b/passes/opt/Makefile.inc
index e7b62fc6a..4a22c2301 100644
--- a/passes/opt/Makefile.inc
+++ b/passes/opt/Makefile.inc
@@ -32,6 +32,7 @@ $(eval $(call add_extra_objs,passes/opt/peepopt_pm.h))
 PEEPOPT_PATTERN  = passes/opt/peepopt_shiftmul_right.pmg
 PEEPOPT_PATTERN += passes/opt/peepopt_shiftmul_left.pmg
 PEEPOPT_PATTERN += passes/opt/peepopt_shiftadd.pmg
+PEEPOPT_PATTERN += passes/opt/peepopt_shiftpow2.pmg
 PEEPOPT_PATTERN += passes/opt/peepopt_muldiv.pmg
 PEEPOPT_PATTERN += passes/opt/peepopt_muldiv_c.pmg
 PEEPOPT_PATTERN += passes/opt/peepopt_formal_clockgateff.pmg
diff --git a/passes/opt/peepopt.cc b/passes/opt/peepopt.cc
index fa7cf74a0..ac5b571f7 100644
--- a/passes/opt/peepopt.cc
+++ b/passes/opt/peepopt.cc
@@ -68,6 +68,12 @@ struct PeepoptPass : public Pass {
 		log("                limits the amount of padding to a multiple of the data, \n");
 		log("                to avoid high resource usage from large temporary MUX trees.\n");
 		log("\n");
+		log("   * shiftpow2 - Replace A>>(B<<K) with a $bmux word multiplexer when\n");
+		log("                the output width is at most the stride 1<<K. This handles\n");
+		log("                power-of-two aligned word selects.\n");
+		log("                Scratchpad: 'peepopt.shiftpow2.max_data_multiple' (default: 2)\n");
+		log("                limits padding for out-of-range select values.\n");
+		log("\n");
 		log("If -formalclk is specified it instead employs the following rules:\n");
 		log("\n");
 		log("   * clockgateff - Replace latch based clock gating patterns with a flip-flop\n");
@@ -115,6 +121,7 @@ struct PeepoptPass : public Pass {
 					pm.run_shiftadd();
 					pm.run_shiftmul_right();
 					pm.run_shiftmul_left();
+					pm.run_shiftpow2();
 					pm.run_muldiv();
 					pm.run_muldiv_c();
 				}
diff --git a/passes/opt/peepopt_shiftpow2.pmg b/passes/opt/peepopt_shiftpow2.pmg
new file mode 100644
index 000000000..f65e62f17
--- /dev/null
+++ b/passes/opt/peepopt_shiftpow2.pmg
@@ -0,0 +1,87 @@
+pattern shiftpow2
+//
+// Optimize shifts that result from expressions such as foo[s*W+:W]
+// when W is a power of two and the multiply has been folded away.
+//
+
+match shift
+	select shift->type.in($shift, $shiftx, $shr)
+	filter !port(shift, \B).empty()
+endmatch
+
+code
+{
+	// make sure the shift amount cannot be negative
+	SigSpec amount = port(shift, \B);
+	bool b_signed = shift->type.in($shift, $shiftx) && param(shift, \B_SIGNED).as_bool();
+	if (!b_signed)
+		amount.append(State::S0);
+	if (amount.bits().back() != State::S0)
+		reject;
+
+	while (GetSize(amount) > 1 && amount.bits().back() == State::S0)
+		amount.remove(GetSize(amount) - 1);
+
+	// low zero bits encode the power-of-two scale
+	int log2scale = 0;
+	while (!amount.empty() && amount[0] == State::S0) {
+		amount.remove(0);
+		log2scale++;
+	}
+
+	if (log2scale < 1)
+		reject;
+
+	if (amount.empty() || amount.is_fully_const())
+		reject;
+
+	SigSpec sel = amount;
+	int sel_width = GetSize(sel);
+	int width = param(shift, \Y_WIDTH).as_int();
+	if (log2scale >= 8 * (int)sizeof(int) - 1)
+		reject;
+	int stride = 1 << log2scale;
+
+	// avoid overlapping selections
+	if (width > stride)
+		reject;
+
+	if (sel_width > 20)
+		reject;
+	long long ways = 1LL << sel_width;
+
+	SigSpec A = port(shift, \A);
+	int a_width = GetSize(A);
+	bool a_signed = !shift->type.in($shiftx) && param(shift, \A_SIGNED).as_bool();
+	int extended_a_width = a_signed ? std::max(a_width, width) : a_width;
+
+	// limit padding for out-of-range select values
+	int max_ratio = module->design->scratchpad_get_int("peepopt.shiftpow2.max_data_multiple", 2);
+	if (ways * (long long)width > (long long)max_ratio * std::max(a_width, width))
+		reject;
+
+	did_something = true;
+	log("shiftpow2 pattern in %s: shift=%s, index=%s, stride=%d, width=%d, ways=%lld\n",
+			module, shift, log_signal(sel), stride, width, ways);
+
+	// way m holds A[m*stride +: width], way 0 in the LSBs
+	State fill = shift->type.in($shiftx) ? State::Sx : State::S0;
+	SigSpec bmux_a;
+	for (long long m = 0; m < ways; m++) {
+		long long base = m * (long long)stride;
+		for (int b = 0; b < width; b++) {
+			long long idx = base + b;
+			if (idx < a_width)
+				bmux_a.append(A[idx]);
+			else if (idx < extended_a_width)
+				bmux_a.append(A.back());
+			else
+				bmux_a.append(fill);
+		}
+	}
+
+	module->addBmux(NEW_ID, bmux_a, sel, port(shift, \Y));
+	autoremove(shift);
+	accept;
+}
+endcode
diff --git a/tests/various/peepopt.ys b/tests/various/peepopt.ys
index cbbd477e8..e0b9946cf 100644
--- a/tests/various/peepopt.ys
+++ b/tests/various/peepopt.ys
@@ -8,8 +8,8 @@ prep -nokeepdc
 equiv_opt -assert peepopt
 design -load postopt
 clean
-select -assert-count 1 t:$shiftx
-select -assert-count 0 t:$shiftx t:* %D
+select -assert-count 1 t:$bmux
+select -assert-count 0 t:$bmux t:* %D
 
 ####################
 
@@ -72,9 +72,10 @@ design -import gate -as gate peepopt_shiftmul_3
 miter -equiv -make_assert -make_outputs -ignore_gold_x -flatten gold gate miter
 sat -verify -show-public -enable_undef -prove-asserts miter
 cd gate
-select -assert-count 1 t:$shr
-select -assert-count 1 t:$mul
-select -assert-count 0 t:$shr t:$mul %% t:* %D
+clean
+select -assert-count 1 t:$bmux
+select -assert-count 0 t:$shr
+select -assert-count 0 t:$mul
 
 ####################
 
@@ -92,3 +93,155 @@ equiv_opt -assert peepopt
 design -load postopt
 clean
 select -assert-count 0 t:*
+
+####################
+
+# shiftpow2: a power-of-two part-select i[s*W+:W] becomes a $bmux word mux
+design -reset
+read_verilog <<EOT
+module peepopt_shiftpow2_0 #(parameter M=8, parameter W=4) (input [M*W-1:0] i, input [$clog2(M)-1:0] s, output [W-1:0] o);
+assign o = i[s*W+:W];
+endmodule
+EOT
+
+prep -nokeepdc
+equiv_opt -assert peepopt
+design -load postopt
+clean
+select -assert-count 1 t:$bmux
+select -assert-count 0 t:$bmux t:* %D
+
+####################
+
+# shiftpow2: explicit aligned right shift D >> (S*8), checked by SAT miter
+design -reset
+read_verilog <<EOT
+module peepopt_shiftpow2_1 (input [63:0] D, input [2:0] S, output [7:0] Y);
+	assign Y = D >> (S*8);
+endmodule
+EOT
+
+prep
+design -save gold
+peepopt
+design -stash gate
+
+design -import gold -as gold peepopt_shiftpow2_1
+design -import gate -as gate peepopt_shiftpow2_1
+
+miter -equiv -make_assert -make_outputs -ignore_gold_x -flatten gold gate miter
+sat -verify -show-public -enable_undef -prove-asserts miter
+cd gate
+clean
+select -assert-count 1 t:$bmux
+select -assert-count 0 t:$shr
+
+####################
+
+# shiftpow2: width smaller than stride is non-overlapping
+design -reset
+read_verilog <<EOT
+module peepopt_shiftpow2_narrow (input [31:0] D, input [2:0] S, output [3:0] Y);
+	assign Y = D >> (S*8);
+endmodule
+EOT
+
+prep
+design -save gold
+peepopt
+design -stash gate
+
+design -import gold -as gold peepopt_shiftpow2_narrow
+design -import gate -as gate peepopt_shiftpow2_narrow
+
+miter -equiv -make_assert -make_outputs -ignore_gold_x -flatten gold gate miter
+sat -verify -show-public -enable_undef -prove-asserts miter
+cd gate
+clean
+select -assert-count 1 t:$bmux
+select -assert-count 0 t:$shr
+
+####################
+
+# shiftpow2: signed part-select with out-of-range padding
+design -reset
+read_verilog <<EOT
+module peepopt_shiftpow2_signed (input signed [15:0] i, input [2:0] s, output [3:0] o);
+	assign o = i[s*4 +: 4];
+endmodule
+EOT
+
+prep
+# drive wreduce to a fixed point before checking for the reduced shift
+wreduce
+design -save gold
+peepopt
+design -stash gate
+
+design -import gold -as gold peepopt_shiftpow2_signed
+design -import gate -as gate peepopt_shiftpow2_signed
+
+miter -equiv -make_assert -make_outputs -ignore_gold_x -flatten gold gate miter
+sat -verify -show-public -enable_undef -prove-asserts miter
+cd gate
+clean
+select -assert-count 1 t:$bmux
+select -assert-count 0 t:$shiftx
+
+####################
+
+# shiftpow2: signed $shr extends A to Y_WIDTH
+design -reset
+read_verilog <<EOT
+module peepopt_shiftpow2_signed_shr (input signed [3:0] D, input S, output [7:0] Y);
+	assign Y = D >> (S*8);
+endmodule
+EOT
+
+prep
+design -save gold
+peepopt
+design -stash gate
+
+design -import gold -as gold peepopt_shiftpow2_signed_shr
+design -import gate -as gate peepopt_shiftpow2_signed_shr
+
+miter -equiv -make_assert -make_outputs -flatten gold gate miter
+sat -verify -show-public -prove-asserts miter
+cd gate
+clean
+select -assert-count 1 t:$bmux
+select -assert-count 0 t:$shr
+
+####################
+
+# shiftpow2 must NOT fire for overlapping selections
+design -reset
+read_verilog <<EOT
+module peepopt_shiftpow2_overlap (input [31:0] D, input [1:0] S, output [7:0] Y);
+	assign Y = D >> (S*4);
+endmodule
+EOT
+
+prep -nokeepdc
+peepopt
+clean
+select -assert-count 0 t:$bmux
+select -assert-count 1 t:$shr
+
+####################
+
+# shiftpow2: shiftmul can expose a non-overlapping power-of-two stride
+design -reset
+read_verilog <<EOT
+module peepopt_shiftpow2_shiftmul #(parameter M=8, parameter W=3) (input [M*W-1:0] i, input [2:0] s, output [W-1:0] o);
+assign o = i[s*W+:W];
+endmodule
+EOT
+
+prep -nokeepdc
+equiv_opt -assert peepopt
+design -load postopt
+clean
+select -assert-count 1 t:$bmux
+select -assert-count 0 t:$bmux t:* %D