In this paper, we answer the question when inserting label noise (less informative labels) can instead return us more accurate and fair models. We are primarily inspired by two observations that 1) increasing a certain class of instances label noise to balance the noise rates (increasing-to-balancing) results in an easier learning problem; 2) Increasing-to-balancing improves fairness guarantees against label bias. In this paper, we will first quantify the trade-offs introduced by increasing a certain group of instances label noise rate w.r.t. the learning difficulties and performance guarantees. We analytically demonstrate when such an increase proves to be beneficial, in terms of either improved generalization errors or the fairness guarantees. Then we present a method to leverage our idea of inserting label noise for the task of learning with noisy labels, either without or with a fairness constraint. The primary technical challenge we face is due to the fact that we would not know which data instances are suffering from higher noise, and we would not have the ground truth labels to verify any possible hypothesis. We propose a detection method that informs us which group of labels might suffer from higher noise, without using ground truth information. We formally establish the effectiveness of the proposed solution and demonstrate it with extensive experiments.