In planning tasks, conditional effects model action outcomes that depend on the current state of the world. Conditional effects are a crucial modeling feature since compiling them away can cause an exponential growth in task size. However, only a few admissible heuristics support them. To add abstraction heuristics to this set, we show how to compute projections, Cartesian abstractions and merge-and-shrink abstractions for tasks with conditional effects. Our experiments show that these heuristics are competitive with, and often surpass, the state-of-the-art for conditional-effect tasks.