Mr Byers said the pair needed to sell, or release from tie, a handful of their outlets in 17 local licensing areas to reduce their individual holdings below 25 per cent of the market. Both agreed to comply with the directive.
Punch Taverns bought Allied's estate in August for pounds 2.75bn, and under the deal sold on 550 of the larger pubs to Bass for about pounds 1bn. Earlier this month, the Department of Trade and Industry imposed similar small- scale conditions on Scottish & Newcastle to clear its pounds 1.14bn buyout of 821 pubs from Greenalls.
"Bass is willing to give the appropriate undertakings which relate to local concentrations of pub ownership in four out of 505 licensing districts," the brewer said, adding that about 20 pubs would be affected.
Punch Taverns, which is privately held, also said it would rejig its estate to meet Mr Byers' demands, with about 30 pubs affected in 13 local areas.
Mr Byers had threatened to refer the deals to the Competition Commission unless Bass and Punch had agreed to address his concerns within six months.
Separately, Mr Byers cleared Punch's pounds 69m takeover of Inn Business' 788 tenanted pubs.
Bass shares rose 40p yesterday to 675p.