"Higher" log-lin model produces worse fit?


I would really appreciate some pointers on this:

a log-linear model that produces better fit with fewer terms. E.g. in a 3D scenario I have
Model 1: A+B+C
Model 2: AB+C

And in some cases I find that Model 1 has better fit. (just to be clear, by better fit I mean it has a higher p-value, not a lower Chi-square value - I do realise the Chi-squares are not directly comparable.)

Somehow I just always assumed that a "higher" model would always improve the fit - the fact that in all the examples I can find in my books that is always the case may have had something to do with this :)

Any pointers to literature that touches upon such issues would be extremely welcome.