Counterfactual examples explain a prediction by highlighting changes of instance that flip the outcome of a classifier. This paper proposes TIGTEC, an efficient and modular method for generating sparse, plausible and diverse counterfactual explanations for textual data. TIGTEC is a text editing heuristic that targets and modifies words with high contribution using local feature importance. A new attention-based local feature importance is proposed. Counterfactual candidates are generated and assessed with a cost function integrating semantic distance, while the solution space is efficiently explored in a beam search fashion. The conducted experiments show the relevance of TIGTEC in terms of success rate, sparsity, diversity and plausibility. This method can be used in both model-specific or model-agnostic way, which makes it very convenient for generating counterfactual explanations.