Ch’ol (Mayan) exhibits asymmetries in what is available for left branch extraction. While both numerals and interrogative possessors are able to extract from absolutive subject position, only numerals may extract from absolutive object position. To capture this asymmetry, I provide evidence that objects with overt possessors always undergo object shift, blocking left branch extraction. This follows from the Freezing Principle ( Ross 1974; Wexler & Culicover 1977), or a ban on extraction from a moved constituent. Objects with numeral modifiers do not obligatorily undergo object shift and therefore may extract from the object. In addition to numerals and interrogative possessors, I present and analyze possibilities for other elements to extract out of various positions. I situate this work within Agree-based theories of extraction (e.g. Rackowski & Richards 2005; van Urk & Richards 2015; Branan 2018) and discuss this proposal’s theoretical implications. Unless otherwise noted, all data comes from the author’s fieldwork.