The 3 basic data types of contaminant hydrology are examined by stochastic modelling of a groundwater contamination case. The stochastic transport model, which is of the Monte Carlo type, uses a numerical flow and transport model, and views transmissivity as a random autocorrelated field. A large set of transmissivity realisations is generated using the turning bands technique. Conditioning is done with regard to transmissivity, head and concentration observations. The unconditional approach assumes, explicitly, a stationary stochastic process of logtransmissivity. This is implicitly turned into a non-stationary process by the conditioning procedures. These use simple and universal kriging, and utilize the kriging uncertainties to determine subsets of realisations that are in agreement with the observations at a predefined confidence level. The approach followed allows quantification of the uncertainties of predicted head and concentration through space and time. Conditioning on head observations leaves large transport uncertainties. Conditioning on the transmissivity data has a more prominent effect. The single, most effective data type is the concentration data. Smallest transport uncertainties occur when all the data are simultaneously taken into account. The conditioning effect depends on the number and spatial configuration of the data. A trade-off between the stochastic and deterministic transport approach is suggested. In modelling terms this corresponds to a trade-off between advection and dispersion.