Originally Posted by anabolism

The main limitation on how optimal the results will be is Matrix's timeout. We on the outside don't know Matrix's internal structure so we can only guess as to the effect of various limitations we add in the query. Some limitations presumably allow Matrix to narrow the initial set of flight/fare options it considers, while others presumably force it to do more work later in selecting flights. From the results you're getting, it would seem that adding an "alliance" extension code narrows the initial set of flights, allowing Matrix to better search them for the lowest fare. I've found that in some cases, adding specific flights to the extension codes causes Matrix to return "No flights found," even though without those specific flight restrictions, the results will include those flights. I can guess from this that adding specific flight restrictions caused Matrix to do more processing later, during which it timed out before it found results that had those flights.