As Pichia pastoris (syn. Komagataella sp.) yeast can secrete pure recombinant proteins at high rates, it is a desirable production system. The function of a novel synthetic variant of the AOX1 promoter was characterised comprehensively using a strain secreting Candida antarctica lipase B (CALB) as a model. A new time-saving approach was introduced to determine, in only one experiment, the hitherto unknown relationship between specific product formation rate (q p) and specific growth rate (μ). Tight control of recombinant protein formation was possible in the absence of methanol, while using glycerol as a sole carbon/energy source. CALB was not synthesised during batch cultivation in excess glycerol (>10 g l−1) and at a growth rate close to μ max (0.15 h−1). Between 0.017 and 0.115 h−1 in glycerol-limited fedbatch cultures, basal levels of q p > 0.4 mg g−1 h−1 CALB were reached, independent of the μ at which the culture grew. At μ > 0.04 h−1, an elevated q p occurred temporarily during the first 20 h after changing to fedbatch mode and decreased thereafter to basal. In order to accelerate the determination of the q p(μ) relationship (kinetics of product formation), the entire μ range was covered in a single fedbatch experiment. By linearly increasing and decreasing glycerol addition rates, μ values were repeatedly shifted from 0.004 to 0.074 h−1 and vice versa. Changes in q p were related to changes in μ. A rough estimation of μ range suitable for production was possible in a single fedbatch, thus significantly reducing the experimental input over previous approaches comprising several experiments.