Mass spectrum analysis
Generally speaking: knowing the history of your sample (e.g. earlier steps of synthesis allowing / excluding elements that could numerically fit into the list of suggested fragments) and additional spectroscopic characterisation (UV-Vis, IR, Raman, NMR, etc.) may be helpful.

The problem you describe may be attenuated by using a mass spectrometer of higher resolving power.  Instead of submitting the sample to the detector behind a smaller LC-MS coupled analysis, providing a purified sample to a larger, tuneable sector mass spectrometer, for example.

An important alternative is coupling of several mass spectrometers along one line, where after initial ionisation primary fragments are separated from each other, and their corresponding subsequently generated daughter fragments are eventually characterised, like in a tandem MS/MS:



(source)

An overview about the later provides this wikipedia entry.