We make use of 9 yr of full-disc helioseismic data - as collected by the ground-based Birmingham Solar-Oscillations Network (BiSON) - to search for low-frequency, low-angular-degree (low-ℓ) acoustic modes. A range of tests are applied to the power spectrum of the observations that search for prominent mode-like structure: strong spikes, structure spanning several bins signifying the presence of width (from damping), and the occurrence of prominent multiplet structure at ℓ ≥ 1 arising principally from the solar rotation and made from several spikes separated suitably in frequency. For each test we present analytical expressions that allow the probability that the uncovered structure is part of the broad-band noise background to be assessed. These make use of the cumulative binomial (Bernoulli) distribution and serve to provide an objective measure of the significance of the detections. This work has to date uncovered nine significant detections of non-broad-band origin that we have identified as low-ℓ modes with radial overtone numbers n ≤ 9.