diff --git a/src/CodeGen_X86.cpp b/src/CodeGen_X86.cpp
index df8065212193..bcf401bb07be 100644
--- a/src/CodeGen_X86.cpp
+++ b/src/CodeGen_X86.cpp
@@ -495,6 +495,31 @@ void CodeGen_X86::visit(const Call *op) {
         return;
     }
 
+    // A 16-bit mul-shift-right of less than 16 can sometimes be rounded up to a
+    // full 16 to use pmulh(u)w by left-shifting one of the operands. This is
+    // handled here instead of in the lowering of mul_shift_right because it's
+    // unlikely to be a good idea on platforms other than x86, as it adds an
+    // extra shift in the fully-lowered case.
+    if ((op->type.element_of() == UInt(16) ||
+         op->type.element_of() == Int(16)) &&
+        op->is_intrinsic(Call::mul_shift_right)) {
+        internal_assert(op->args.size() == 3);
+        const uint64_t *shift = as_const_uint(op->args[2]);
+        if (shift && *shift < 16 && *shift >= 8) {
+            Type narrow = op->type.with_bits(8);
+            Expr narrow_a = lossless_cast(narrow, op->args[0]);
+            Expr narrow_b = narrow_a.defined() ? Expr() : lossless_cast(narrow, op->args[1]);
+            int shift_left = 16 - (int)(*shift);
+            if (narrow_a.defined()) {
+                codegen(mul_shift_right(op->args[0] << shift_left, op->args[1], 16));
+                return;
+            } else if (narrow_b.defined()) {
+                codegen(mul_shift_right(op->args[0], op->args[1] << shift_left, 16));
+                return;
+            }
+        }
+    }
+
     struct Pattern {
         string intrin;
         Expr pattern;
diff --git a/src/FindIntrinsics.cpp b/src/FindIntrinsics.cpp
index 1b91da64f587..16cd2432a98c 100644
--- a/src/FindIntrinsics.cpp
+++ b/src/FindIntrinsics.cpp
@@ -384,6 +384,7 @@ class FindIntrinsics : public IRMutator {
             auto is_x_same_int = op->type.is_int() && is_int(x, bits);
             auto is_x_same_uint = op->type.is_uint() && is_uint(x, bits);
             auto is_x_same_int_or_uint = is_x_same_int || is_x_same_uint;
+            auto is_y_narrow_uint = op->type.is_uint() && is_uint(y, bits / 2);
             if (
                 // Saturating patterns
                 rewrite(max(min(widening_add(x, y), upper), lower),
@@ -493,6 +494,25 @@ class FindIntrinsics : public IRMutator {
                         rounding_mul_shift_right(x, y, cast(unsigned_type, c0)),
                         is_x_same_int_or_uint && c0 >= bits) ||
 
+                // We can also match on smaller shifts if one of the args is
+                // narrow. We don't do this for signed (yet), because the
+                // saturation issue is tricky.
+                rewrite(shift_right(widening_mul(x, cast(op->type, y)), c0),
+                        mul_shift_right(x, cast(op->type, y), cast(unsigned_type, c0)),
+                        is_x_same_int_or_uint && is_y_narrow_uint && c0 >= bits / 2) ||
+
+                rewrite(rounding_shift_right(widening_mul(x, cast(op->type, y)), c0),
+                        rounding_mul_shift_right(x, cast(op->type, y), cast(unsigned_type, c0)),
+                        is_x_same_int_or_uint && is_y_narrow_uint && c0 >= bits / 2) ||
+
+                rewrite(shift_right(widening_mul(cast(op->type, y), x), c0),
+                        mul_shift_right(cast(op->type, y), x, cast(unsigned_type, c0)),
+                        is_x_same_int_or_uint && is_y_narrow_uint && c0 >= bits / 2) ||
+
+                rewrite(rounding_shift_right(widening_mul(cast(op->type, y), x), c0),
+                        rounding_mul_shift_right(cast(op->type, y), x, cast(unsigned_type, c0)),
+                        is_x_same_int_or_uint && is_y_narrow_uint && c0 >= bits / 2) ||
+
                 // Halving subtract patterns
                 rewrite(shift_right(cast(op_type_wide, widening_sub(x, y)), 1),
                         halving_sub(x, y),
diff --git a/test/correctness/intrinsics.cpp b/test/correctness/intrinsics.cpp
index bc5764f5d7f8..f978a7956a14 100644
--- a/test/correctness/intrinsics.cpp
+++ b/test/correctness/intrinsics.cpp
@@ -308,6 +308,9 @@ int main(int argc, char **argv) {
     check(i8(i16(i8x) * i16(i8y) >> 8), mul_shift_right(i8x, i8y, 8));
     check(u8(u16(u8x) * u16(u8y) >> 8), mul_shift_right(u8x, u8y, 8));
 
+    // Multiplication of mixed-width integers
+    check(u16(u32(u16x) * u32(u8y) >> 8), mul_shift_right(u16x, u16(u8y), 8));
+
     check(i8_sat(rounding_shift_right(i16(i8x) * i16(i8y), 7)), rounding_mul_shift_right(i8x, i8y, 7));
     check(i8(min(rounding_shift_right(i16(i8x) * i16(i8y), 7), 127)), rounding_mul_shift_right(i8x, i8y, 7));
     check(i8_sat(rounding_shift_right(i16(i8x) * i16(i8y), 8)), rounding_mul_shift_right(i8x, i8y, 8));
diff --git a/test/correctness/simd_op_check.cpp b/test/correctness/simd_op_check.cpp
index f82df01147ac..fa51ac99d917 100644
--- a/test/correctness/simd_op_check.cpp
+++ b/test/correctness/simd_op_check.cpp
@@ -117,6 +117,13 @@ class SimdOpCheck : public SimdOpCheckTest {
 
             check("pmulhuw", 4 * w, i16_1 / 15);
 
+            // Shifts by amounts other than 16 can also use this instruction, by
+            // preshifting an arg (when there are bits of headroom), or
+            // postshifting the result.
+            check("pmulhuw", 4 * w, u16((u32(u16_1) * u32(u8_2)) >> 13));
+            check("pmulhw", 4 * w, i16((i32(i16_1) * i32(i16_2)) >> 17));
+            check("pmulhuw", 4 * w, u16((u32(u16_1) * u32(u16_2)) >> 18));
+
             if (w > 1) {  // LLVM does a lousy job at the comparisons for 64-bit types
                 check("pcmp*b", 8 * w, select(u8_1 == u8_2, u8(1), u8(2)));
                 check("pcmp*b", 8 * w, select(u8_1 > u8_2, u8(1), u8(2)));