Prior studies have noted a strongly nonlinear enhancement of lightning flash rates with increasing cloud height. Here we report a related observation, of a tendency for increasing intracloud-discharge radiofrequency-emission power for increased height of the electrified cloud. The FORTE satellite's radio-frequency-receiver payload has performed extensive recordings of electromagnetic emissions of lightning discharges. The most commonly occurring such emission arises from intracloud electrical breakdown and is usually recognizable by a pulse followed by a delayed echo from the ground reflection. We have used other systems of lightning monitors to provide source locations for an extended data set of FORTE intracloud-discharge signals. The interpulse separation within each pulse pair yields the discharge height above the reflective ground. The storm in which the pulse occurs usually provides many (at least 50) recorded events. From the pattern of these events' heights, we can usually infer a capping height, which serves as an upper bound on the lightning discharge heights for that storm. We find that there is a strong statistical increase of effective radiated power of intracloud discharges, for increasing capping height of the parent storm. Thus a future satellite-based lightning monitor that triggers on only the most intense radiofrequency emissions will be strongly selective for electrified storms with very deep vertical development. Such storms are also indicated in severe convective weather.