diff --git a/asm/encode.go b/asm/encode.go
index da976ba..94da113 100644
--- a/asm/encode.go
+++ b/asm/encode.go
@@ -184,8 +184,11 @@ func (e *enc) encode(mnem string, ops []Operand) error {
 			return fmt.Errorf("RETFL expects an immediate")
 		}
 		return e.emit(&instr{opcode: []byte{0xCA}, modrm: -1, sib: -1, imm: le16(int64(imm))})
-	// MOVDQ2Q/MOVQ2DQ cross the MMX and XMM banks (F2 0F D6), the register
-	// in the reg field, the other bank's in r/m.
+	// MOVDQ2Q/MOVQ2DQ cross the MMX and XMM banks, and each direction
+	// carries its own mandatory prefix: the toolchain renders F3 0F D6 as
+	// MOVQ2DQ (the MMX source, XMM destination) and F2 0F D6 as MOVDQ2Q
+	// (the XMM source, MMX destination), the register in the reg field, the
+	// other bank's in r/m.
 	case "MOVDQ2Q", "MOVQ2DQ":
 		if len(ops) != 2 {
 			return fmt.Errorf("%s expects 2 operands, got %d", upper, len(ops))
@@ -199,7 +202,11 @@ func (e *enc) encode(mnem string, ops []Operand) error {
 			upper == "MOVQ2DQ" && (!srcReg.mmx || !dstReg.isVec()) {
 			return fmt.Errorf("%s crosses the XMM and MMX banks in that order", upper)
 		}
-		i := &instr{prefix: 0xF2, opcode: []byte{0x0F, 0xD6}, modrm: -1, sib: -1}
+		prefix := byte(0xF2)
+		if upper == "MOVQ2DQ" {
+			prefix = 0xF3
+		}
+		i := &instr{prefix: prefix, opcode: []byte{0x0F, 0xD6}, modrm: -1, sib: -1}
 		if err := setRM(i, dstReg, srcReg, 8); err != nil {
 			return err
 		}
diff --git a/asm/rendered_text_test.go b/asm/rendered_text_test.go
index e3fe9e1..3232043 100644
--- a/asm/rendered_text_test.go
+++ b/asm/rendered_text_test.go
@@ -24,6 +24,9 @@ func TestRenderedTextEncodes(t *testing.T) {
 		// The segment-absolute rendering lowers to the FS-prefixed disp32
 		// absolute, exactly what the 0(FS) spelling encodes.
 		{"MOVQ FS:0, DX", "64488b142500000000"},
+		// The bank-crossing quadword move takes the prefix by direction: the
+		// MMX source carries F3, the XMM source F2.
+		{"MOVQ2DQ M2, X11", "f3440fd6da"},
 	} {
 		src := "TEXT \u00b7k(SB), NOSPLIT, $0\n\t" + tt.text + "\n\tRET\n"
 		f, errs := parser.Parse("k.s", src)