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We introduce and study level-planar straight-line drawings with a fixed number λ of slopes. For proper level graphs, we give an O(n log^2 n / loglog n)-time algorithm that either finds such a drawing or determines that no such drawing exists. Moreover, we consider the partial drawing extension problem, where we seek to extend an immutable drawing of a subgraph to a drawing of the whole graph, and the simultaneous drawing problem, which asks about the existence of drawings of two graphs whosearXiv:1907.13558v1 fatcat:a6mtdmeqgfdbvlmvgjn4nm323y