MRI of tissues with short transverse relaxation times raises both scientific and clinical interest and can be performed with zero echo time MRI. However, as RF excitation is done under the radial encoding gradient, flip angle amplitudes and uniformity are limited. This issue can be circumvented by using longer modulated pulses. However, pulse length is limited by dead-time-induced central k-space gaps getting too large for robust image reconstruction. In this work, we propose a new approach that enables the use of long RF pulses in algebraic ZTE by utilizing their intrinsic encoding properties to fill part of the dead-time gap.