Web surveys have several advantages compared to more traditional surveys with in-person interviews, telephone interviews, or mail surveys. Their most obvious potential drawback is that they may not be representative of the population of interest because the sub-population with access to Internet is quite specific. This paper investigates propensity scores as a method for dealing with selection bias in web surveys. Our main example has an unusually rich sampling design, where the Internet sample is drawn from an existing much larger probability sample that is representative of the US 50+ population and their spouses (the Health and Retirement Study). We use this to estimate propensity scores and to construct weights based on the propensity scores to correct for selectivity. We investigate whether propensity weights constructed on the basis of a relatively small set of variables are sufficient to correct the distribution of other variables so that these distributions become representative of the population. If this is the case, information about these other variables could be collected over the Internet only. Using a backward stepwise regression we find that at a minimum all demographic variables are needed to construct the weights. The propensity adjustment works well for many but not all variables investigated. For example, we find that correcting on the basis of socio-economic status by using education level and personal income is not enough to get a representative estimate of stock ownership. This casts some doubt on the common procedure to use a few basic variables to blindly correct for selectivity in convenience samples drawn over the Internet. Alternatives include providing non-Internet users with access to the Web or conducting web surveys in the context of mixed mode surveys.