Displacement-encoded imaging with stimulated echoes (DENSE) and harmonic phase imaging (HARP) employ 1-1 spatial modulation of magnetization to cosine modulate the longitudinal magnetization as a function of position at end diastole. Later in the cardiac cycle they sample the cosine-modulated signal and compute myocardial strain from the signal phase. The sampled signal generally includes three distinct echoes: 1) a displacement-encoded stimulated echo, 2) the complex conjugate of the displacement-encoded echo, and 3) an echo arising from T1 relaxation. If the T1-relaxation and complex conjugate echoes are suppressed, then a phase image representing just the displacement-encoded echo can be reconstructed. In the present study, the use of cosine and sine modulation to eliminate (CANSEL) the T1-relaxation and complex conjugate echoes was investigated. With the use of CANSEL, it was demonstrated that DENSE accurately measures through-plane as well as in-plane components of tissue motion. Also, DENSE with CANSEL artifact suppression can provide increased signal-to-noise ratio (SNR) secondary to reduced intravoxel dephasing by using relatively low displacement-encoding frequencies. For applications that employ DENSE imaging with multiple acquisitions, the CANSEL technique can suppress artifact-generating echoes without placing constraints on the displacement-encoding frequency and direction.