Trade-off between transient response and grid-side current quality is a well-known issue of single-phase mains-connected power converters. A dual-loop control structure (usually based on PI or type-II controllers) is typically employed in such systems to regulate the DC link voltage to a constant reference (in order to maintain power balance) while forcing the grid-side current to have a specific shape (in order to comply with power quality requirements). Introducing notch term/s (tuned to certain multiple/s of the mains base frequency) into one of the loops allows either for the improvement of the dynamic performance without worsening the total harmonic distortion of grid-side current or for the enhancement of the current quality without impairing the dynamic response. Since the maximum tolerable value of total harmonic distortion is typically imposed by a certain power quality standard, it is desirable to enhance the transient response of the power converter system as much as possible while keeping the total harmonic distortion at the maximum allowed value. However, universal off-grid operating power conversion systems must support both 50 Hz and 60 Hz mains; consequently, tuning the notch term/s to 50 Hz multiple/s would not be sufficient for a 60 Hz mains operation and vice-versa. Consequently, this work examines the possibility of introducing a dual-notch term into the control loop in order to cover both above-mentioned base frequencies. It is demonstrated that under typical base frequency uncertainty values, the performances of dual-notch terms are nearly decoupled so that the term tuned to a 50 Hz frequency (and optionally to its multiples) has nearly no influence at a 60 Hz mains operation and vice-versa. Consequently, the methodology allows for the improvement of the dynamics of universal grid-connected power converters without total harmonic distortion (THD) deterioration. A stability analysis of the proposed control structure is carried out and quantitative design guidelines, allowing for the attainment of an optimized dynamic response for a given maximum tolerable total harmonic distortion, minimum allowed phase margin and a certain base frequency uncertainty, are established. It is shown that a DC link voltage loop bandwidth of 52 Hz may be attained while keeping the grid-side current THD below 5%. Simulations and experimental results support well the proposed design methodology.