Two magnetic field tapering concepts for the suppression of backward-wave oscillations in helix traveling-wave tubes (TWTs) are presented. Therefore, the beam-wave interaction in a homogeneous helix section is modified. Increasing the field strength reduces the beam diameter and consequently the beam-wave coupling, while an additional offset in the focusing field alters the synchronism between both. The theoretical background is introduced and results from a 1-D small-signal and a 3-D particle-in-cell code are presented and compared. Furthermore, a concept to apply the suppression techniques to a complete TWT is presented, and the influence on the amplifier output characteristics is analyzed.