  We present a mechanism for efficiency increase in quantum heat engines
containing internal energy levels that do not couple to the external work sink.
The gain is achieved by using these levels to channel heat in a direction
opposite to the one dictated by the second law. No quantum coherence, quantum
correlations or ergotropy are required. A similar mechanism allows the engine
to run in reverse and still produce useful work. We illustrate these ideas
using a simple quantum Otto cycle in a coupled-spin system. We find this engine
also exhibits other counterintuitive phenomenology. For example, its efficiency
may increase as the temperature difference between the heat baths decreases.
Conversely, it may cease to operate if the hotter bath becomes too hot or the
colder bath too cold.
