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Summary form only given. Relative intensity noise (RIN) in vertical cavity surface emitting lasers (VCSELs) is important for applications in communications and optical interconnections. It is known that VCSELs tend to lase at high powers in multiple transverse modes due to spatial hole burning (SHE). This behavior can increase the RIN and limit the usefulness of VCSELs in high-speed communications. In the paper it is found that low RIN operation can be maintained for low spatially overlapping modes.