Motivated by problems of ranking with partial information, we introduce a variant of the cascading bandit model that considers flexible length sequences with varying rewards and losses. We formulate two generative models for this problem within the generalized linear setting, and design and analyze upper confidence algorithms for it. Our analysis delivers tight regret bounds which, when specialized to standard cascading bandits, results in sharper guarantees than previously available in the literature. We evaluate our algorithms against a representative sample of cascading bandit baselines on a number of real-world datasets and show significantly improved empirical performance.