It is widely accepted that a quantum computer will need some form of protection against decoherence, and to date the only tool capable of providing fault-tolerance is quantum error correction (QEC). Here we study the interplay of Dynamical decoupling (DD), an open-loop non-fault-tolerant capable decoherence suppression method, and Quantum error correction codes. Several schemes exist where DD is used to improve gate fidelities, such as Dynamically Protected Gates or (Concatenated) Dynamically Corrected Gates. Several authors have combined DD and QEC with different degrees of success, showing improved gate fidelity but at the cost of, in cases strong, extra locality constraints on the error model or a sequence size which is exponential in the number of physical qubits (n). In this work we introduce a dynamical sequences that use as pulses elements of the stabilizer and the normalizer of the QEC code (SXDD sequences). We show how this idea can be adapted to the leading DD schemes: Concatenated DD and Nested Uhrig DD. With this we avoid the need for further locality constraints and obtain shorter sequences while still obtaining fidelity improvements. Moreover, the fact that the SXDD pulses can be chosen to be bitwise allows a natural integration with fault-tolerant methods and the direct porting of several DD schemes for fidelity-enhanced gates into the SXDD scenario.