Prior research in neurally-inspired perceptron predictors and Geometric History Length-based TAGE predictors has shown significant improvements in branch prediction accuracy by exploiting correlations in long branch histories. However, not all branches in the long branch history provide useful context. Biased branches resolve as either taken or not-taken virtually every time. Including them in the branch predictor's history does not directly contribute any useful information, but all existing history-based predictors include them anyway. In this work, we propose Bias-Free branch predictors that are structured to learn correlations only with non-biased conditional branches, aka. branches whose dynamic behavior varies during a program's execution. This, combined with a recency-stack-like management policy for the global history register, opens up the opportunity for a modest history length to include much older and much richer context to predict future branches more accurately. With a 64KB storage budget, the Bias-Free predictor delivers 2.49 MPKI (mispredictions per 1000 instructions), improves by 5.32% over the most accurate neural predictor and achieves comparable accuracy to that of the TAGE predictor with fewer predictor tables or better accuracy with same number of tables. This eventually will translate to lower energy dissipated in the memory arrays per prediction.