This work presents a novel attenuation imaging technique for pulse-echo ultrasound systems. In contrast to state-of-the-art techniques, we formulate the reconstruction in two dimensions relying on tissue insonifications with different steering angles. By beamforming backscattered echoes recorded by the transducer, we measure at each location the changes in the amplitudes of detected echoes with different transmissions and relate them to local tissue attenuation. This relationship assumes ultrasound waves propagate in straight paths; thus, we linearize the forward problem to provide suitable time-to-solutions for clinical practice. The presented technique is the natural extension of computed tomography in echo mode (CUTE), initially developed for tissue speed-of-sound quantification. The performance of our method is demonstrated in numerical examples with data computed using the k-Wave numerical solver for wave-propagation simulations. These examples consider tissue-mimicking media with varying heterogeneity in attenuation and echogenicity. The results show that our method can provide images with promising spatial and contrast resolution, as well as attenuation estimates independent of tissue echogenicity. This work represents a necessary first step towards multi-modal CUTE imaging of speed of sound and attenuation in tissue.