Studies of binary pulsars provide insight into various theories of physics. Detection of such systems is challenging due to the Doppler modulation of the pulsed signal caused by the orbital motion of the pulsar. We investigated the loss of sensitivity in eccentric binary systems for different types of companions. This reduction of sensitivity should be considered in future population synthesis models for binary pulsars. This loss can be recovered partially by employing the `acceleration search' algorithm and even better by using the `acceleration-jerk search' algorithm.