In this paper, we design, characterize in closed-form, and evaluate a new index rule for Markovian time-varying channels, which gives rise to a simple opportunistic scheduling rule for flow-level scheduling in wireless downlink systems. For user channels, we employ the Gilbert–Elliot model with a flow-level interpretation: the channel condition follows a general two-state Markov chain with distinct probabilities of finishing the flow transmission. The index value of the bad channel condition takes into account both the one-period and the steady-state potential improvement of the service completion probability, while the good channel condition gets an absolute priority with the cμcμ-index (well-known to be throughput-optimal) as the tie-breaking rule. Our computational study confirms near-optimality of the proposed rule in most of the instances, and suggests that information about the channels steady state is often enough to achieve near-optimality.