The present paper discusses a new construction of UWB pulses within the framework of soft-spectrum adaptation. The employed basis functions are B-splines having the following properties: (i) The B-splines are time-limited piecewise polynomials. (ii) The first-order B-splines are rectangular pulses and they converge band-limited functions at the limit that their order tends to infinity. (iii) There are an analog circuit and a fast digital filter for the generation of B-splines. Simple application of Gram-Schmidt orthonormalization process to the shifted B-splines results in a few basic pulses, which are well time-limited and have a broad band width, but do not comply with the FCC spectral mask. A constrained approximation technique is proposed for adaptively designing pulses so that they approximate target frequency characteristics. At the cost of using eleven shifted B-splines, an example set of four pulses comforting the FCC spectral mask is obtained.