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We present a detailed analysis of short-pulse detachment processes using few-cycle pulses with the aim of demonstrating means for controlling such processes. We first generalize the standard Keldysh-type formalism for laser-target interactions (in which final-state interaction between the detached electron and the core is ignored) to include the possibility that the vector potential is nonzero at the end of the interaction between a short laser pulse and the target. With this formalism in hand, we examine the effects of half-cycle pulses (HCPs) on detachment of the prototypical negative ion H–, and show that detachment by pairs of oppositely-directed (i.e., "bidirectional") HCPs allows one to understand the interference pattern seen in detachment by single-cycle pulses. We also examine in detail the transition from few-cycle pulses to many-cycle pulses as various experimental parameters are varied, i.e., the laser frequency, the laser-pulse duration, and the absolute phase of the carrier wave with respect to the pulse envelope. Finally, we examine the use of pairs of single-cycle pulses, differing in phase by 180°, together with a modest static electric field to control coherently the extent of H– detachment as the delay between the pulses is varied. Our simulations show that this scheme allows one to modulate the H– detachment probability by ~30%, which is far higher than has been achieved for similar schemes using many-cycle pulses. Although our results are presented specifically for H–, they apply to detachment of any negative ion having s-state valence electrons; in addition, the qualitative information on half-cycle, single-cycle, and few-cycle pulse interactions should be generally applicable to short-pulse detachment or ionization of other target atoms or ions.