In Spanish, there are cases in which both the matrix TP and the embedded TP are elided all together, leaving apparently one remnant per clause. This paper examines how such kind of complex process of clausal ellipsis can be accounted for in a principled way, taking into consideration the existing analyses of TP-deletion. I argue that complex TP-ellipsis in Spanish is derived by deleting both the matrix TP and the embedded TP without moving the remnants of each TP. I claim that a deletion analysis assuming in-situ remnants is adequate to deal with complex TP-ellipsis and is also supported by the fact that heads like complementizer and negation (or the positive polarity marker si) cannot undergo the alleged movement of the remnant to the specifier of a functional phrase. I also discuss why non-null subject languages like English and French do not allow complex clausal ellipsis of both matrix TP and embedded TP, by claiming that the difference between Spanish and English/French may be attributable to the presence/absence of (some sort of) the so-called Comp-trace effects in the context of complex TP-ellipsis.