The presence of an extended blue horizontal branch (HB) in a stellar population is known to affect the age inferred from spectral fitting to stellar population synthesis models. This is due to the hot blue component which increases the strength of the Balmer lines and can make an old population look spuriously young. However, most population synthesis models still rely on theoretical isochrones, which do not include realistic modelling of extended HBs. In this work, we create detailed models for a range of old simple stellar populations (SSPs), with metallicities ranging from [Fe/H]=−1.3 to solar, to create a variety of realistic HB morphologies, from extended red clumps, to extreme blue HBs. We achieve this by utilizing stellar tracks from the BaSTI data base and implementing a different mass-loss prescription for each SSP created. This includes setting an average mass and a Gaussian spread in masses of individual stars coming on to the zero-age HB for each model, and hence resulting in different HB morphologies. We find that, for each metallicity, there is some HB morphology which maximizes Hβ, making an underlying 14-Gyr population look ∼5–6 Gyr old for the low- and intermediate-metallicity cases, and as young as 2 Gyr in the case of the solar metallicity SSP. We explore whether there are any spectral indices capable of breaking the degeneracy between an old SSP with extended blue HB and a truly young or intermediate-age SSP, and find that the Ca ii index of Rose and the strength of the Mg ii doublet at 2800 Å are promising candidates, in combination with Hβ and other metallicity indicators, such as Mgb and Fe5406. We also run Monte Carlo simulations to investigate the level of statistical fluctuations in the spectra of typical stellar clusters. We find that fluctuations in spectral indices are significant even for average to large globular clusters and that various spectral indices are affected in different ways, which has implications for full-spectrum fitting methods. Hence, we urge caution if these types of stellar clusters are to be used as empirical calibrating objects for various aspects of stellar population synthesis models.