In machine learning applications, there is a need to obtain predictive models of high performance and, most importantly, to allow end-users and practitioners to understand and act on their predictions. One way to obtain such understanding is via counterfactuals, that provide sample-based explanations in the form of recommendations on which features need to be modified from a test example so that the classification outcome of a given classifier changes from an undesired outcome to a desired one. This paper focuses on the domain of time series classification, more specifically, on defining counterfactual explanations for univariate time series. We propose Glacier, a model-agnostic method for generating locally-constrained counterfactual explanations for time series classification using gradient search either on the original space or on a latent space that is learned through an auto-encoder. An additional flexibility of our method is the inclusion of constraints on the counterfactual generation process that favour applying changes to particular time series points or segments while discouraging changing others. The main purpose of these constraints is to ensure more reliable counterfactuals, while increasing the efficiency of the counterfactual generation process. Two particular types of constraints are considered, i.e., example-specific constraints and global constraints. We conduct extensive experiments on 40 datasets from the UCR archive, comparing different instantiations of Glacier against three competitors. Our findings suggest that Glacier outperforms the three competitors in terms of two common metrics for counterfactuals, i.e., proximity and compactness. Moreover, Glacier obtains comparable counterfactual validity compared to the best of the three competitors. Finally, when comparing the unconstrained variant of Glacier to the constraint-based variants, we conclude that the inclusion of example-specific and global constraints yields a good performance while demonstrating the trade-off between the different metrics. © The Author(s) 2024.