Reliable detection and tracking of eyes is an important requirement for attentive user interfaces. In this paper, we present an innovative approach to the problem of eye tracking. A number of traditional eye detectors, chosen for their own properties, are combined by two different competitive schemes with the aim to obtain a higher degree of robustness and reliability. To illustrate our work and validate our competitive combination approach, we introduce a proof-of-concept single-camera remote eye tracker and discuss its implementation and the produced experimental results.