In this paper a simple but very general method is given for estimating a population total with any sampling design when objects in sampled units are observed with imperfect detectability--a problem characteristic of many surveys of natural and human populations. In the most general case, the method consists of dividing the value of the variable of interest associated with each detected object by the detection probability for that object and then proceeding to use the estimation method that would ordinarily be used under the design if there were no detectability problems. Examples illustrating the method include simple random sampling, conventional unequal probability sampling, and adaptive cluster sampling.