Invalid combination of opcodes and operands when cmov pointer and register

I want to write a piece of code in assembly language, that would change all uppercase characters in a string to lowercase. However, I would like to avoid as many conditional jumps as possible. I tried the following code:

    global tolower_cmov

tolower_cmov:
    enter 0, 0
    mov edx, [ebp + 8]
    xor eax, eax
    xor ecx, ecx
.back:
    test [edx], byte 0xff
    jz .end

    mov eax, [edx]
    mov ecx, [edx]
    add [eax], byte 'a' - 'A'
    cmp [edx], byte 'A'
    cmovb [edx], eax
    cmp [edx], byte 'z'
    cmova [edx],  ecx

    inc edx
    jmp .back
.end:
    leave
    ret

But NASM gives me Invalid combination of opcodes and operands error on both CMOV lines... I don't understand, what is wrong with those lines?

With the help of Michael, I have managed to find a solution, that suits my needs:

    global tolower_cmov

tolower_cmov:
    enter 0, 0
    mov edx, [ebp + 8]
.back:
    test [edx], byte 0xff
    jz .end

    xor eax, eax
    xor ecx, ecx

    mov eax, [edx]
    mov ecx, [edx]
    add ecx, dword 'a' - 'A'
    cmp [edx], byte 'A'
    cmovb ecx, eax
    cmp [edx], byte 'Z'
    cmova ecx, eax
    mov [edx], ecx

    inc edx
    jmp .back
.end:
    leave
    ret