At least since 1980 when Deaton and Muellbauer's famous Almost Ideal Demand System (AIDS) was published, the emphasis in applied demand analysis has been on a flexible specification of substitution effects. Recent theoretical work by Cooper and McLaren (1992a&b) and Cooper, McLaren and Parameswaran (1993) has put more emphasis on effectively globally regular systems which allow greater flexibility in the treatment of Engel effects. Current empirical work (e.g., Chatterjee and Ray, 1992) continues to use a relatively inflexible treatment of Engel effects. Following Lewbel's (1991) lead, in the present paper we attempt to evaluate the need for a more flexible treatment by examining Engel effects in the Australian Household Expenditure Survey for 1988-89 from an agnostic position in which the form of the Engel response is entirely data-determined. We do this using non-parametric procedures in the statistical package S-Plus. Contrary to common practice (and confirming Lewbel's empirical results for U.K. and U.S. data), we find evidence of non-monotonic responses of budget shares with increasing income. This argues in favour of more flexible forms for Engel curves such as those explored by Rimmer and Powell (1992a&b) (or more generally, in recent work by Cooper and McLaren). Using the same methodology, we also carry out a brief exploration of the influence of demographic effects on household Engel responses.