Bulgarian solitaire is played on n cards divided into several piles; a move consists of picking one card from each pile to form a new pile. This can be seen as a process on the set of integer partitions of n: If sorted configurations are represented by Young diagrams, a move in the solitaire consists of picking all cards in the bottom layer of the diagram and inserting the picked cards as a new column. Here we consider a generalization, L-solitaire, wherein a fixed set of layers L (that includes the bottom layer) are picked to form a new column. L-solitaire has the property that if a stable configuration of n cards exists it is unique. Moreover, the Young diagram of a configuration is convex if and only if it is a stable (fixpoint) configuration of some L-solitaire. If the Young diagrams representing card configurations are scaled down to have unit area, the stable configurations corresponding to an infinite sequence of pick-layer sets (L1, L2, . . .) may tend to a limit shape φ. We show that every convex φ with certain properties can arise as the limit shape of some sequence of Ln. We conjecture that recurrent configurations have the same limit shapes as stable configurations. For the special case Ln = {1, 1 + ⌊1/qn⌋, 1 + ⌊2/qn⌋, . . . }, where the pick layers are approximately equidistant with average distance 1/qn for some qn ∈ (0, 1], these limit shapes are linear (in case nq2n → 0), exponential (in case nq2n → ∞), or interpolating between these shapes (in case nq2n → C > 0).