Observations of the Sun with the LOWL instrument provide a homogeneous set of solar p-mode frequencies from low to intermediate degree that allow one to determine the structure of much of the solar interior avoiding systematic errors that are introduced when different data sets are combined, i.e., principally the effects of solar cycle changes on the frequencies, Unfortunately, the LOWL data set contains very few of the lowest-degree modes, which are essential for determining reliably the structure of the solar core - in addition, these lowest-degree data have fairly large associated uncertainties, However, observations made by the Birmingham Solar-Oscillations Network (BiSON) in integrated sunlight provide high-accuracy measurements of a large number of low-degree modes. In this paper we demonstrate that the low-degree mode set of the LOWL data can be successfully combined with the more accurate BiSON data, provided the observations are contemporaneous for those frequencies where the solar cycle induced effects are important, We show that this leads to a factor of 2 decrease in the error on the inferred sound speed in the solar core, We find that the solar sound speed is higher than in solar models for r < 0.2 R.. The density of the solar core is, however, lower than that in solar models.