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Carbon nanotubes have extraordinary mechanical properties, but modifications of their structure tend to weaken them. Here, we have studied by experiments and modelling the one-dimensional filling of single chirality (6,5) carbon nanotubes with iodine and water. We show that iodine-filling can enhance the pressure of radial collapse of these nanotubes by a factor 2 compared to the empty (6,5) tubes. For water filling, this enhancement factor reduces to 1.4. Our single-chirality study allows correlating the different Raman signatures of the radial collapsing process, which was not possible in samples with mixed chiralities. A clear spectroscopic signature of the collapse pressure can thus be given: it is the pressure at which the G-band frequency evolution with pressure softens while the radial breathing mode intensity vanishes. These new criteria for the detection of radial collapse allow correcting some existing discrepancies in the literature. Finally, we discuss the impact of molecular filling on the radial mechanical stability as a function of the tube diameter. It results that molecular filling allows for a superior stability effect than filling with tubes (i.e. multi-wall carbon nanotubes). The stability enhancement tends to grow with the tube diameter and depends strongly on the nature of the filling molecules.