A fundamental brain computation is to identify the best in a set of noisy or uncertain options, which is required for inference, decision-making, optimization, action selection, consensus, and foraging. To solve these problems, noisy observations need to be integrated over time to evaluate, compare, and choose from them. This process involves allocating attention or other finite neuronal resources dynamically over the alternatives to make the best choice. The problem of allocating finite resources has been recently studied under the context of the so-called breadth-depth (BD) dilemma, but how finite resources should be divided and dynamically allocated over options in an optimal manner is not known. Here, we introduce a novel perspective, designing a recurrent neural network to deal with the BD dilemma from a dynamical point of view. A key hallmark of our model lies in a dynamical noise reduction: during the noisy evidence accumulation, the noise magnitude is regulated by the number of active units, such that less noisy observations result from attending to a lower number of alternatives. This noise reduction embodies the capability of our brain to rearrange its finite attentional or neuronal resources along the decision processes. The combination of non-linearity, integration, and number-dependent noise reduction results in a close to optimal network performance. We find that it is best to initially divide attention into many alternatives (resembling a form of a pre-attentive mechanism) later followed by a drastic reduction to a handful of attended alternatives (resembling focused attention). Our modelling approach can offer a unifying framework to study the dynamical aspects of attention in many-alternatives decision-making.