  The computation of the glueball spectrum is particularly challenging due to
the rapid decay of the signal-to-noise ratio of the correlation functions. To
address this issue, advanced techniques such as gauge link smearing and the
variational method are commonly employed to identify the spectrum before the
signal diminishes significantly. However, a significant improvement in the
signal-to-noise ratio can be achieved by utilising multilevel sampling
techniques. In this talk, we present a study of the glueball spectrum in pure
gauge theory with a two-level algorithm. Specifically, we explore the relation
between noise reduction and the various multilevel parameters, such as the
width of the dynamical regions and the number of submeasurements.
