In this paper we evaluate the effects of hard and soft constraints on the Iterative Data Snooping (IDS), an iterative outlier elimination procedure. Here, the measurements of a levelling geodetic network were classified according to the local redundancy and maximum absolute correlation between the outlier test statistics, referred to as clusters. We highlight that the larger the relaxation of the constraints, the higher the sensitivity indicators MDB (Minimal Detectable Bias) and MIB (Minimal Identifiable Bias) for both the clustering of measurements and the clustering of constraints. There are circumstances that increase the family-wise error rate (FWE) of the test statistics, increase the performance of the IDS. Under a scenario of soft constraints, one should set out at least three soft constraints in order to identify an outlier in the constraints. In general, hard constraints should be used in the stage of pre-processing data for the purpose of identifying and removing possible outlying measurements. In that process, one should opt to set out the redundant hard constraints. After identifying and removing possible outliers, the soft constraints should be employed to propagate their uncertainties to the model parameters during the process of least-squares estimation.