  Results from a partial-wave analysis of the reaction $\gamma p \rightarrow
K^+ \Lambda$ are presented. The reaction is dominated by the $S_{11}(1650)$ and
$P_{13}(1720)$ resonances at low energies and by $P_{13}(1900)$ at higher
energies. There are small contributions from all amplitudes up to and including
$G_{17}$, with $F_{17}$ necessary for obtaining a good fit of several of the
spin observables. We find evidence for $P_{11}$(1880), $D_{13}$(2120), and
$D_{15}$(2080) resonances, as well as a possible $F_{17}$ resonance near 2300
MeV, which is expected from quark-model predictions. Some predictions for
$\gamma n \to K^0 \Lambda$ are also included.
