Well, first to guess what your requirements might be - from the information you provide, you are looking for a 1xCR123A physically fairly small light that starts on a lower level than the P1D. But you also want the possibility of higher output modes and are willing to accept a clicky (knowing it will add a bit to the length of the flashlight) to get all you want. I am also guessing you want the higher output levels to be pretty powerful.
I think then maybe the P2D (latest version with Q5) should fit the bill?
It is a bit longer and has a reverse clicky, but it starts at a low level (with further depressions of the switch getting you higher outputs, and eventually an SOS mode - there is also control via the bezel, which you rotate to get a turbo mode plus a strobe).
Using manufacturer's estimates, the P2D starts with a low of 12 lumens, whereas the P1D starts out at 96 lumens, and you need to change output levels twice to get an output level of 16 lumens.
So that's something you can consider that could fit your various requirements.
The other possibilities in a non-Fenix line would probably include flashlights with memory modes where you could leave the light off in your desired low output level. Not sure if you want to go there, since there is a bit of a time penalty since if you use the flashlight in any other mode, you'd have to switch back to low before going off. Probably best to get a light that always comes on where you most want it without any need for action on your part.