NOVELTY - Treating cellulose-containing material involves: (a1) treating first mixture (M1) comprising the material and aqueous first acid having first concentration (C1) with first dilute acid under conditions including first temperature (T1); (a2) treating second mixture (M2) comprising material treated in step (a1) and aqueous second acid having second concentration (C2) with second dilute acid under conditions including second temperature (T2), where (T2) is greater than (T1), (C2) is greater than (C1) or (M1) has consistency greater than (M2); and (a3) subjecting to mechanical size reduction.    USE - In the treatment of cellulose-containing material such as wood chips (claimed) used for the production of cellulosic ethanol and other alcohol fuels, and in pulp and paper industry. The bioconversion of lignocellulose to alcohol fuel also allows for the production of value-added biomaterials and biochemicals such as furfural, acetic acid and lignin.    ADVANTAGE - The method efficiently uses chemical processes in combination with disc-refiner to decrease biomass recalcitrance, increase digestibility ad reduce energy consumption during mechanical size reduction. The method reduces net specific energy consumed in mechanical size reduction step by at least 95% when compared to disc refining of untreated wood chips. The method allows production of glucose at a yield of at least 70% (preferably at least 90%) in presence of 15 FPU/g glucan. The method is commercially viable, is simple, avoids use of large scale reactors, and is economical, and has low operational cost.    DETAILED DESCRIPTION - Treating a cellulose-containing material involves: (a1) treating a first mixture (M1) comprising the material and an aqueous first acid having a first concentration (C1) with a first dilute acid under a first set of conditions including a first treatment temperature (T1); (a2) treating a second mixture (M2) comprising the material treated in step (a1) and an aqueous second acid having a second concentration (C2) with a second dilute acid under a second set of conditions including a second treatment temperature (T2), where at least one of the following conditions is met: i) the temperature (T2) is greater than temperature (T1), ii) the concentration (C2) is greater than concentration (C1), and iii) the mixture (M1) has consistency that is greater than consistency of mixture (M2); and (a3) subsequent to step (a1), subjecting the material to mechanical size reduction.