An extension to the sparsity promoting iterated constrained endmember (SPICE) algorithm, named as SPICEE, has been presented. In ICE and SPICE, endmembers are estimated using a pseudoinverse method, which may generate endmembers that are not physically possible when representing normalized reflectance spectra. Although this problem can be alleviated by increasing the regularization, too much regularization leads to finding erroneous endmembers. To solve these problems, in this letter, a quadratic optimization solution is proposed that constrains the endmembers to have values between zero and one. The results on three data sets indicate that when regularization is large enough, SPICE and SPICEE generate similar answers; and when regularization is small to none, SPICEE stays more robust. In doing so, besides generating realistic endmembers, SPICEE helps in decreasing the effort necessary for fine-tuning the regularization parameter.