Camera-traps are a versatile and widely adopted tool for collecting biological data for wildlife conservation and management. While estimating population abundance from camera-trap data is the primarily goal of many projects, the question of which population estimator is suitable for analysing these data needs to be investigated. We took advantage of a 21 day camera-trap monitoring period of giraffes (\textit{Giraffa camelopardalis angolensis}) on the Ongava Game Reserve (Namibia) to compare capture-recapture (CR), rarefaction curves and $N$-mixture estimators of population abundance. A marked variation in detection probability of giraffes was observed both in time and between individuals, with a skewed occurrence of animals at some waterholes. The mean daily visit frequency of waterholes by giraffes was $f = 0.25$ although they were less likely to be detected after they were seen at a waterhole. We estimated the population size to be 104 giraffes ($C_v = 0.02$) using the most robust reference estimator (CR). All other estimators deviated from the CR population size by \textit{ca.} $-16$ to $>+106$\%. This was due the fact that these models did not account for the temporal and individual variations in detection probability. We found that modelling choice was much less forgiving for $N$-mixture models than CR estimators because the former leads to very variable and inconsistent estimations of abundance. Double counts were problematic for $N$-mixture models, challenging the use of raw counts (\textit{i.e.} when individuals are not identified), to monitor the abundance of giraffe or of other species without idiosyncratic coat patterns.