  We include p-spin interactions in a spherical version of a soluble mean-field
spin-glass model proposed by van Hemmen. Due to the simplicity of the
solutions, which do not require the use of the replica trick, we are able to
carry out a detailed investigation of a number of special situations. For p
larger or equal to 3, there appear first-order transitions between the
paramagnetic and the ordered phases. In the presence of additional
ferromagnetic interactions, we show that there is no stable mixed phase, with
both ferromagnetic and spin-glass properties.
