Speckle tracking by normalized cross correlation (NCC) requires subsample accuracy for effective strain estimation. Without this, low displacement causes quantized images that result in unusable strain maps. Doppler methods work well on small displacement, however they operate very poorly on large displacement data where they are prone to aliasing. When manually palpating the medium, it is difficult to maintain a constant deformation rate and pressure, resulting in a mixture of large and small displacement data throughout a total data set. This paper presents the Constrained Radio Frequency method (CRF) of speckle tracking. This method uses the correlation gradients at the sample level to constrain the subsample search region such that the RF data can be interpolated to accurately estimate displacement with subsample precision. Simulated and experimental data sets are used to estimate displacement and strain to compare the CRF method to NCC speckle tracking and the Loupas algorithm doppler technique. The CRF is the most accurate method at estimating displacement and generates strain estimates with higher contrast to noise ratios (CNR) compared to the other methods tested.