A magnetic core structure for a transducer head of the type used in digital data storage devices is wider on one side of the magnetic gap (e.g., the write side) than it on the other side of the gap (e.g., the read side), to provide "wide write-arrow read" recording and reproducing capabilities. Magnetic flux return during recording (writing) operations is accomplished through the comparatively narrow read core plus additional magnetic closure elements which are disposed alongside, and which magnetically shunt, the read core, such that the overall core structure has basically the same width on each side of the magnetic gap. Improved transducing performance is provided by using additional thickness for such magnetic shunts and recessing the end extremity of the latter adjacent the gap at the face of the head, where the head accesses the magnetic recording media, such that the overall magnetic reluctance of the magnetic returns (i.e., shunts) is lowered but the effective gap width of the head is not changed.