AB S TRAC TComplex organic molecules (COMs) have been identified in different environments in starforming regions. Laboratory studies show that COMs form in the solid state, on icy grains, typically following a 'non-energetic' (atom-addition) or 'energetic' (UV-photon absorption) trigger. So far, such studies have been largely performed for single processes. Here, we present the first work that quantitatively investigates both the relative importance and the cumulative effect of '(non-)energetic' processing. We focus on astronomically relevant CO:CH3OH = 4:1 ice analogues exposed to doses relevant for the collapse stage of dense clouds. Hydrogenation experiments result in the formation of methyl formate (MF; HC(O)OCH3), glycolaldehyde (GA; HC(O)CH2OH) and ethylene glycol (EG; H2C(OH)CH2OH) at 14 K. The absolute abundances and the abundance fractions are found to be dependent on the H-atom/CO:CH3 OHmolecule ratios and on the overall deposition rate. In the case that ices are exposed to UV photons only, several different COMs are found. Typically, the abundance fractions are 0.2 for MF, 0.3 for GA and 0.5 for EG as opposed to the values found in pure hydrogenation experiments without UV in which MF is largely absent: 0.0, 0.2-0.6 and 0.8-0.4, respectively. In experiments where both are applied, overall COM abundances drop to about half of those found in the pure UV irradiation experiments, but the composition fractions are very similar. This implies COM ratios can be used as a diagnostic tool to derive the processing history of an ice. Solid-state branching ratios derived here for GA and EG compare well with observations, while the MF case cannot be explained by solid-state conditions investigated here.