A method for determining mantissa bit allocation of frequency domain audio data to be encoded, including by performing adaptive low frequency compensation on each frequency band of a set of low frequency bands of the data. The low frequency compensation includes steps of: performing tonality detection on the audio data to generate compensation control data indicative of whether each frequency band in the set has prominent tonal content; and performing low frequency compensation on each frequency band in the set having prominent tonal content, including by correcting a preliminary masking value for each frequency band having prominent tonal content, but not performing low frequency compensation on the audio data in any other frequency band in the set; wherein the frequency domain audio data comprises an exponent value for said each low frequency band of the set, and the tonality detection includes determining, for said each low frequency band of the set, a measure of difference between exponents and corresponding tented exponents of the audio data. Other aspects are audio encoding methods including such tonality detection and low frequency compensation steps, and a system configured to perform any embodiment of the inventive method.