You would think, given the vast tribe of verbal compounds with inter- as a prefix, that a few species of intrā-compounds would also inhabit that wood of the Latin dictionary. In fact, they are highly endangered, perhaps even extinct. Here are a few compound adjectives and nouns that I discovered; the verbs were nowhere to be found.
Consider section 121a4, which lists a variety of consonant stem adjectives that do not take -i in the ablative singular. They are completely regular, and the entry is really there only to keep you from having second guesses.
I’ll list them here so they get some web mileage, despite not being especially interesting, however rare:
caeles, caelitis relating to the heavens or their Gods
compos, compotis possessing control of
dēses, dēsidis lazy
dīves, dīvitis wealthy
hospes, hospitis amicable, relating to guest-friendship
particeps, participis participating in
praepes, praepitis nimble, winged
pauper, pauperis poor, destitute
prīnceps, prīncipis princely, noble
sōspes, sospitis safe and sound
superstes, superstitis surviving
As someone pointed out in a comment, the general but non-binding idea is that those adjectives which most often operate as nouns (like these) take the ablative in -e, whereas those that are properly adjectival take the ablative in -i. You find hints of this throughout the consonantal and i-stem entries in Allen and Greenough (see 121a1-2), but they make no effort to propagate it as a formal rule.