Flux-calibrated integrated spectra have been obtained for a sample of 16 blue compact and high surface brightness Large Magellanic Cloud (LMC) star clusters. The spectra cover the wavelength range 3700-6800 angstrom, with a typical resolution and dispersion of 14 angstrom and 3.5 angstrom/pixel, respectively. We simultaneously derive foreground E(B - V) reddening values and ages for the clusters by comparing the line strengths and continuum distribution of their integrated spectra with those of LMC cluster spectra templates. As a first approach to obtain cluster ages, we also use the equivalent width (EW) of Balmer absorption lines and some diagnostic diagrams involving the sum of the EWs of selected spectral lines. Through evolutionary synthesis models for simple stellar populations and using a full-spectrum fitting code, we also derive reddenings, ages, and metallicities (Z/Z(circle dot)) for the cluster sample. No metallicity determinations have been previously performed for nine out of the 16 clusters here studied. We find good agreement between the cluster ages derived from the template-matching method and those ages estimated from theoretical evolutionary synthesis models. All of the studied clusters are found to be young, with ages ranging from 15 Myr (NGC 1693) to 80 Myr (NGC 2160), affected by reddening values typical for the LMC: 0.00 < E (B - V) < 0.20. The derived metallicities Z/Z(circle dot) range from 0.2 up to 1.0 (solar metal content). We compare our results with those reported in the literature, and discuss the distribution of metallicity values. In an effort to create a spectral library at LMC metallicity level with several clusters per age range, the present cluster sample stands out as a useful complement to previous ones.