We discuss a novel method of efficiently producing multiphoton states using repeated spontaneous parametric down-conversion. Specifically, by attempting down-conversion several times, we can pseudodeterministically add photons to a mode, producing various several-photon states, e.g., Fock states and N00N states (number-path entangled states of the form |N(A), 0(B)>+|0(A), N(B)>). This scheme is exponentially more efficient than previous proposals; we discuss expected performance and experimental limitations.