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In a very recent work by Tang and Maitra, a theoretical construction of balanced functions f on n-variables (n \equiv 2 mod 4) with very good autocorrelation and Walsh spectra values (absolute indicator \Delta_f < 2n/2 and nolinearity nl( f ) > 2^(n-1) - 2^(n/2) + 2^(n/2-3) - 5.2^(n-2)/4) have been presented [IEEE-IT, 64(1):393-402, 2018]. The theoretical bounds could be satisfied for all such n \geq 46. At the same time it has also been pointed out that though theoretically not proved, such constructions may provide further interesting examples of Boolean functions. In our study, we revisit the construction and apply search methods in suitable places to obtain balanced functions on even variables in the interval [10, …, 26] with improved parameters that could never be achieved before. In fact, for the first time we could provide examples of balanced Boolean functions f having \Delta_f < 2^(n/2) for n \equiv 0 mod 4, where n = 12, 16, 20, and 24. Whatever functions we attain have nonlinearity greater than 2^(n-1) - 2^(n/2).