To solve deep metric learning problems and producing feature embeddings, current methodologies will commonly use a triplet model to minimise the relative distance between samples from the same class and maximise the relative distance between samples from different classes. Though successful, the training convergence of this triplet model can be compromised by the fact that the vast majority of the training samples will produce gradients with magnitudes that are close to zero. This issue has motivated the development of methods that explore the global structure of the embedding and other methods that explore hard negative/positive mining. The effectiveness of such mining methods is often associated with intractable computational requirements. In this paper, we propose a novel deep metric learning method that combines the triplet model and the global structure of the embedding space. We rely on a smart mining procedure that produces effective training samples for a low computational cost. In addition, we propose an adaptive controller that automatically adjusts the smart mining hyper-parameters and speeds up the convergence of the training process. We show empirically that our proposed method allows for fast and more accurate training of triplet ConvNets than other competing mining methods. Additionally, we show that our method achieves new state-of-the-art embedding results for CUB-200-2011 and Cars196 datasets.