  Experiments studying vibrational effects on electronic transport through
single molecules have observed several seemingly inconsistent behaviors,
ranging from up to 30 harmonics of a vibrational frequency in one experiment,
to an absence of higher-harmonic peaks in another. We study the different
manifestations of electronic-vibrational coupling in inelastic and elastic
electron transport through single molecules. For the case of inelastic
transport, higher harmonics are shown to be damped by additional small factors
beyond powers of the electron-vibration coupling constant $\lambda$. Two
mechanisms greatly increase the size of secondary peaks in inelastic transport:
coupling between electron transport and spatial motion of the molecule, and the
``pumping'' of higher vibrational modes of the molecule when vibrational
excitations do not completely relax between electron transits.
