  We present an exact calculation of $S$ and $P$ wave $QQ\bar n\bar n$ states
using different standard nonrelativistic quark--quark potentials. We explore in
detail the charm and bottom sectors looking for bound states that could be
measured within existing facilities. Against the proliferation of four--quark
states sometimes predicted in the literature, we found a small number of
candidates to be stable. We analyze their properties in a trial to distinguish
between compact and molecular states. Possible decay modes are discussed.
