We report Doppler measurements of the stars HD 187085 and HD 20782 which indicate two high eccentricity low-mass companions to the stars. We find HD 187085 has a Jupiter-mass companion with a ∼1000-d orbit. Our formal 'best-fitting' solution suggests an eccentricity of 0.47, however, it does not sample the periastron passage of the companion and we find that orbital solutions with eccentricities between 0.1 and 0.8 give only slightly poorer fits (based on rms and χ²ν) and are thus plausible. Observations made during periastron passage in 2007 June should allow for the reliable determination of the orbital eccentricity for the companion to HD 187085. Our data set for HD 20782 does sample periastron and so the orbit for its companion can be more reliably determined. We find the companion to HD 20782 has M sin i = 1.77 ± 0.22 MJup, an orbital period of 595.86 ± 0.03 d and an orbit with an eccentricity of 0.92 ± 0.03. The detection of such high-eccentricity (and relatively low-velocity amplitude) exoplanets appears to be facilitated by the long-term precision of the Anglo-Australian Planet Search. Looking at exoplanet detections as a whole, we find that those with higher eccentricity seem to have relatively higher velocity amplitudes indicating higher mass planets and/or an observational bias against the detection of high-eccentricity systems.