Recent studies suggest that Resolution Enhancement Compression (REC) can provide significant improvements in terms of imaging quality over Classical Pulsed (CP) ultrasonic imaging techniques, by employing frequency and amplitude modulated transmitted signals. However the performance of coded excitations methods degrades drastically deeper into the tissue where the attenuation effects become more significant. In this work, a technique that allows overcoming the effects of attenuation on REC imaging is proposed (REC-Opt). It consists in compensating the attenuation effects at each depth in reception. Combined with coherent plane wave compounding (CPWC), REC-Opt was compared to the performance of conventional REC (without attenuation compensation) and CP. With experimental data at 3.25 cm depth in a phantom with an attenuation coefficient slope of 0.5 dB/MHz/cm and using an 8.5 MHz probe, REC-Opt enhanced the bandwidth by 40.6% compared to CP, against an enhancement of only 6% between REC and CP using the same excitation signal designed to provide a 42% increase in bandwidth. The bandwidth enhancements translated into axial resolution improvements of 30% and 3% for REC-Opt vs. CP and REC vs. CP, respectively. This study suggests that REC-Opt is an efficient method to overcome attenuation effects in soft tissues, knowing their attenuation coefficient.