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This paper presents a thorough study of the impact of morphology derivation on N-gram-based Statistical Machine Translation (SMT) models from English into a morphology-rich language such as Spanish. For this purpose, we define a framework under the assumption that a certain degree of morphology-related information is not only being ignored by current statistical translation models, but also has a negative impact on their estimation due to the data sparseness it causes. Moreover, we describe how this information can be decoupled from the standard bilingual N-gram models and introduced separately by means of a well-defined and better informed feature-based classification task. Results are presented for the European Parliament Plenary Sessions (EPPS) English-Spanish task, showing oracle scores based on to what extent SMT models can benefit from simplifying Spanish morphological surface forms for each Part-Of-Speech category. We show that verb form morphological richness greatly weakens the standard statistical models, and we carry out a posterior morphology classification by defining a simple set of features and applying machine learning techniques. In addition to that, we propose a simple technique to deal with Spanish enclitic pronouns. Both techniques are empirically evaluated and final translation results show improvements over the baseline by just dealing with Spanish morphology. In principle, the study is also valid for translation from English into any other Romance language (Portuguese, Catalan, French, Galician, Italian, etc.). The proposed method can be applied to both monotonic and non-monotonic decoding scenarios, thus revealing the interaction between word-order decoding and the proposed morphology simplification techniques. Overall results achieve statistically significant improvement over baseline performance in this demanding task.