Let R be a commutative ring with identity and letMbe anR-module. We examine the situation where for each prime ideal ρof R the set of all ρ-prime submodules ofMis finite. In caseRis Noetherian andMis finitely generated, we prove that this condition is equivalent to there being a positive integernsuch that for every prime ideal ρ ofR, the number of ρ-prime submodules ofMis less than or equal ton. We further show that in this case, there is at most one ρ-prime submodule for all but finitely many prime ideals ρ ofR.