In Fourier transform ion cyclotron resonance (FT/ICR) mass spectrometry, coherent ion cyclotron orbital motion is produced by resonant radio frequency (rf) electric field excitation. However, because the excitation electrodes are of finite dimensions, the desired transverse (to the applied magnetic field) rf electric field is accompanied by an rf electric field component along the z- (magnetic field) direction, resulting in mass-dependent z-ejection and mass-dependent FT/ICR mass spectral peak relative magnitudes. Addition of several "guard wires" of voltage-divided rf amplitude allows the rf electric field to be "shimmed" to near-perfect uniformity. In this paper (see also the accompanying paper by Russell et al.), we introduce two types of rf-shimmed ion traps. In the first type, guard wires are placed only in front of the trapping electrodes. In the second type, guard wire rings are placed inside the detector and trapping electrodes. For either arrangement, simion simulations were used to adjust the rf voltages applied (by use of voltage dividers) to the guard wires or rings so as to produce an optimally uniform rf field within the trap. The virtual elimination of z-excitation is confirmed by plots of magnitude-mode relative peak height vs ICR orbital radius. Because the guard wires (or rings) tend to shield the ions from the trapping electrode potential, the shift in ICR frequency with trapping voltage is also reduced, but not as well as by a screened trap.(ABSTRACT TRUNCATED AT 250 WORDS)