A practical method for scatter and attenuation compensation was employed in thallium-201 myocardial single-photon emission tomography (SPET or ECT) with the triple-energy-window (TEW) technique and an iterative attenuation correction method by using a measured attenuation map. The map was reconstructed from technetium-99m transmission CT (TCT) data. A dual-headed SPET gamma camera system equipped with parallel-hole collimators was used for ECT/TCT data acquisition and a new type of external source named "sheet line source" was designed for TCT data acquisition. This sheet line source was composed of a narrow long fluoroplastic tube embedded in a rectangular acrylic board. After injection of 99mTc solution into the tube by an automatic injector, the board was attached in front of the collimator surface of one of the two detectors. After acquiring emission and transmission data separately or simultaneously, we eliminated scattered photons in the transmission and emission data with the TEW method, and reconstructed both images. Then, the effect of attenuation in the scatter-corrected ECT images was compensated with Chang's iterative method by using measured attenuation maps. Our method was validated by several phantom studies and clinical cardiac studies. The method offered improved homogeneity in distribution of myocardial activity and accurate measurements of myocardial tracer uptake. We conclude that the above correction method is feasible because a new type of 99mTc external source may not produce truncation in TCT images and is cost-effective and easy to prepare in clinical situations.