Two types of non-global bandwidth, which may be calledlocalandvariable,have been defined in attempts to improve the performance of kernel density estimators. In nonparametric regression, local linear fitting has become a method of much popularity. It is natural, therefore, to consider the use of non-global bandwidths in the local linear context, and indeedlocalbandwidths are often used. In this paper, it is observed that a natural proposal in the literature for combiningvariablebandwidths with local linear fitting fails in the sense that the resulting mean squared error properties are those normally associated withlocalrather than variable bandwidths. We are able to understand why this happens in terms of weightings that are involved. We also attempt to investigate how the bias reduction expected of well-chosen variable bandwidths might be achieved in conjunction with local linear fitting.