We present an extension to the Lasso [6] for binary classification problems with ordered attributes. Inspired by the Fused Lasso [5] and the Group Lasso [7, 3] models, we aim to both discover and model runs (contiguous subgroups of the variables) that are highly predictive. We call the extended model LAPS (the Lasso with Attribute Partition Search). Such problems commonly arise in financial and medical domains, where predictors are time series variables, for example. This paper outlines the formulation of the problem, an algorithm to obtain the model coefficients and experiments showing applicability to practical problems of this type.