If you have three non-negotiable home search criteria, it is important to reflect on (or at least be aware of) how much overlap exists between these criteria. 

Above are two examples of this way of thinking about your home search....

The first set of buyers will likely have lots of options (large yellow overlap area) because many homes share these criteria:

The second set of buyers will likely have very few options (small yellow overlap area) because there are very few homes that share these criteria:

These are fictitious illustrations -- they don't represent the actual amount of overlap that does or does not exist based on the criteria noted above -- but you should give some thought to how small of an overlap area you are creating for yourself based on what you are defining as non-negotiable in your home search.

If that area is too small, you'll have very few options to consider, and eventually you may decide to flex a bit on what you had previously considered to be a non-negotiable point.