Photonic quantum-information processing schemes; such as linear optics quantum computing; and other experiments relying on single-photon interference; inherently require complete photon indistinguishability to enable the desired photonic interactions to take place. Mode-mismatch is the dominant cause of photon distinguishability in optical circuits. Here we study the effects of photon wave-packet shape on tolerance against the effects of mode mismatch in linear optical circuits; and show that Gaussian distributed photons with large bandwidth are optimal. The result is general and holds for arbitrary linear optical circuits; including ones which allow for postselection and classical feed forward. Our findings indicate that some single photon sources; frequently cited for their potential application to quantum-information processing; may in fact be suboptimal for such applications.