  We give a short proof that if a non-trivial band sum of two knots results in
a tight fibered knot, then the band sum is a connected sum. In particular, this
means that any prime knot obtained by a non-trivial band sum is not tight
fibered. Since a positive L-space knot is tight fibered, a non-trivial band sum
never yields an L-space knot. Consequently, any knot obtained by a non-trivial
band sum cannot admit a finite surgery.
  For context, we exhibit two examples of non-trivial band sums of tight
fibered knots producing prime knots: one is fibered but not tight, and the
other is strongly quasipositive but not fibered.
