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Here's a trick using xor-

MinMax3 MACRO min:REQ, max:REQ
  cmp   min, max
  jnc @f
  mov   edi, esi
  xchg min,max
  @@:
ENDM

Tx equ MinMax3

align 16
Test3 proc
  ; Read from memory
  movzx     eax, WORD PTR 
  movzx     ebx, WORD PTR 
  movzx     ecx, WORD PTR 
  movzx     edx, WORD PTR 
  mov esi,1
  mov edi,0

  ; Sort the values
  Tx ah,al
  Tx bl,ah
  Tx bh,bl
  Tx cl,bh
  Tx ch,cl
  Tx dl,ch
  Tx dh,dl
  xor edi,esi	; are they the same
  jnz SORT_DONE	; no, so swap was not done, else resets edi to zero	
  Tx ah,al
  Tx bl,ah
  Tx bh,bl
  Tx cl,bh
  Tx ch,cl
  Tx dl,ch
  xor edi,esi
  jnz SORT_DONE
  Tx ah,al
  Tx bl,ah
  Tx bh,bl
  Tx cl,bh
  Tx ch,cl
  xor edi,esi
  jnz SORT_DONE
  Tx ah,al
  Tx bl,ah
  Tx bh,bl
  Tx cl,bh
  xor edi,esi
  jnz SORT_DONE
  Tx ah,al
  Tx bl,ah
  Tx bh,bl
  xor edi,esi
  jnz SORT_DONE
  Tx ah,al
  Tx bl,ah
  Tx ah,al

SORT_DONE:
  ; Write to memory
  shl       ebx, 16
  or        ebx, eax
  shl       edx, 16
  or        edx, ecx
  mov       DWORD PTR , ebx
  mov       DWORD PTR , edx
 
  ret
Test3 EndP

eliminates the xor edi,edi after the terminating condition test.

Yes, of course.  The reason I did it this way is that  mov edi,1 take 5 bytes vs. 2 bytes for mov edi,esi.  Similarly,  xor edi,1 takes 5 bytes vs. 2 for xor edi,esi.  But even more important than the 3 extra bytes is the fact that it is an odd number of bytes, so the following codes start on an odd address rather than an even address until the next test.  It usually doesn't make much difference, but I've found on this screwy athlon of mine that code alignment sometimes makes a big difference.  Time it both ways and make your choice.  Probably not much difference on a pentium, and your xor's are probably faster on a pentium than the xchg I used also.

Originally, you wanted to save all the instruction cycles you could, so a little rearranging of your wrapup saves 1-2 cycles on my cpu-

SORT_DONE:
  ; Write to memory
  shl      ebx, 16
  shl      edx, 16
  or        ebx, eax
  or        edx, ecx
  mov      DWORD PTR , ebx
  mov      DWORD PTR , edx