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In previous work we have presented coFJ, an extension to Featherweight Java that promotes coinductive programming, a sub-paradigm expressly devised to ease high-level programming and reasoning with cyclic data structures. The coFJ language supports cyclic objects and regularly corecursive methods, that is, methods whose invocation terminates not only when the corresponding call trace is finite (as happens with ordinary recursion), but also when such a trace is infinite but cyclic, that is, can be specified by a regular term, or, equivalently, by a finite set of recursive syntactic equations. In coFJ it is not easy to ensure that the invocation of a corecursive method will return a well-defined value, since the recursive equations corresponding to the regular trace of the recursive calls may not admit a (unique) solution; in such cases we say that the value returned by the method call is undetermined. In this paper we propose two new contributions. First, we design a simpler construct for defining corecursive methods and, correspondingly, provide a more intuitive operational semantics. For this coFJ variant, we are able to define a type system that allows the user to specify that certain corecursive methods cannot return an undetermined value; in this way, it is possible to prevent unsafe use of such a value. The operational semantics and the type system of coFJ are fully formalized, and the soundness of the type system is proved.