Cross-step waltz is a graceful floating, swooping style of waltz best suited to moderately slow waltzes (104-120 bpm). It's very popular at Waltz etcetera so my Monday playlists include a good number of cross-steps. Cross-step waltz was popular in the early Twentieth Century, then died out until dance historian and Stanford professor Richard Powers resurrected it. You can read all about cross-step waltz and see a demo on his cross-step waltz page. As Richard writes:
Cross-step waltz is more than a dance step. Cross-step waltz embodies a partnering dynamic, a mindset, and a philosophy. The essential aspects of cross-step waltz, for both the Lead and Follow, are the connection to your partner, creativity, flexibility and adaptability, individuality, and responsorial riffing, with kindness.
A weekly dance since the beginning of 1999, Waltz etcetera is a beloved Seattle tradition. It's a welcoming, noncompetitive mixed social partner dance. The music is mostly waltz and blues, spiced with a little swing, nightclub, Latin and tango. Dress is casual. Come with or without a partner.