A continuously monitored one-unit system, backed by an identical standby unit, is perfectly repaired by an in-house repair person, if achievable within a random or deterministic patience time (DPT), or else by a visiting expert, who repairs one or all failed units before leaving. We study four models in terms of the limiting availability and limiting profit per unit time, using semi-Markov processes, when all distributions are exponential. We show that a DPT is preferable to a random patience time, and we characterize conditions under which the expert should repair multiple failed units (rather than only one failed unit) during each visit. We also extend the method when life- and repair times are non-exponential. Copyright © 2009 John Wiley & Sons, Ltd.