Using molecular dynamics simulations in which we take counterions explicitly into account, we study the behavior of a dilute solution of strongly charged polyelectrolytes in poor solvents. We focus on the chain conformational properties under conditions in which chain-chain interactions can be neglected but the counterion concentration remains finite. We investigate the conformations with regard to the parameters chain length, Coulomb interaction strength, and solvent quality and explore in which regime the competition between short-range hydrophobic interactions and long-range Coulomb interactions leads to pearl-necklace-like structures. We observe that large number and size fluctuations in the pearls and strings lead to only small direct signatures in experimental observables like the single-chain form factor. Furthermore, we do not observe the predicted first-order collapse of the necklace into a globular structure when counterion condensation sets in. We will also show that the pearl-necklace regime is rather small for strongly charged polyelectrolytes at finite densities. Even small changes in the charge fraction of the chain can have a large impact on the conformation due to the delicate interplay between counterion distribution and chain conformation.