Soundness property has been defined as the minimal correctness requirement that every business workflow must meet. The property guarantees the absence of livelocks, deadlocks, and other anomalies that can be detected without exact domain knowledge. In this paper we extend the notion of soundness to grid workflows. In addition to discovering flaws in the control flow, our notion also captures incorrect data flow, as well as incorrect (or redundant) data transfer and data removal activities. We propose several possible definitions, depending on the capabilities of (or the options set in) the middleware.To capture the problem of some data occupying the grid storage space unnecessarily long, we also introduce the concept of workflow niceness. Niceness should not be seen as a correctness requirement, but rather as a desired property complementary to soundness. In addition to giving a procedure to check niceness, we also give a method that converts a grid workflow into a "nice" one. By using the language of Petri nets as foundation, we ensure that our results apply to a wide variety of grid workflow languages.