When possible, put the search box or the links into a non-scrolling region so that they remain in place when users scroll down within the index.
If you add letters and links, omit those letters in the index for which there’s no entry.
If space is limited, use a narrow font. If you use Verdana for the topic text, Arial is a good choice for the index entries. Use the same font size as for the topic text.
Within the list of index entries, make the subheadings for each letter visually prominent so that readers can identify each section clearly even while scrolling. Use bold font style and an increased space before the paragraph. Indent subentries.
The following picture contrasts some different implementations:

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