Summary: Kurtosis, usually as measured by the standardised fourth central moment, has been examined on a number of occasions by observing the effect of contaminating the distribution, that is, mixing in another distribution. However, superficial treatment can lead, and indeed has led, to misunderstandings. This paper considers, firstly for a symmetric distribution contaminated at two points symmetrically placed around its centre and then for a mixture of two continuous symmetric distributions, the behaviour of three measures of kurtosis. This is done in general and not just as the mixing proportion tends to zero as in the influence function approach. It is seen that when both scale and kurtosis change, the latter is not necessarily intuitive. It is also illustrated that parameter interpretation in terms of distributional properties such as shape can be misleading without the use of the appropriate distributional partial ordering.