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We explore the statistical and economic importance of restrictions on the dynamics of risk compensation from the perspective of a real-time Bayesian learner who predicts bond excess returns using dynamic term structure models (DTSMs). The question on whether potential statistical predictability offered by such models can generate economically significant portfolio benefits out-of-sample, is revisited while imposing restrictions on their risk premia parameters. To address this question, we propose a methodological framework that successfully handles sequential model search and parameter estimation over the restriction space in real time, allowing investors to revise their beliefs when new information arrives, thus informing their asset allocation and maximising their expected utility. Empirical results reinforce the argument of sparsity in the market price of risk specification since we find strong evidence of out-of-sample predictability only for those models that allow for level risk to be priced and, additionally, only one or two of these risk premia parameters to be different than zero. Most importantly, such statistical evidence is turned into economically significant utility gains, across prediction horizons, different time periods and portfolio specifications. In addition to identifying successful DTSMs, the sequential version of the stochastic search variable selection (SSVS) scheme developed can be applied on its own and also offer useful diagnostics monitoring key quantities over time. Connections with predictive regressions are also provided.