We give approximate solutions for some problems in polyelectrolyte theory involving nonuniform charge distributions. Distributions of condensed counterions and electrostatic free energies are found for line-charge models of oligomers, end segments, junctions separating regions of different charge densities, and two semi-infinite line charges approaching each other end-on. The end-on potential of mean force in the latter case is screened by the Debye length. With that exception, we find little correlation between the Debye screening length and the much smaller distances marking the onset of significant end effects. We suggest a biological application to DNA unwinding by helicases.