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I know of multibib and some related packages but, as far as I understand, they do not seem to fit perfectly my needs.

I would like to do the following. A main bibliography would list all items cited in the main text. A second bibliography will list all items cited in footnotes (and, ideally, in other designated environments, such as remarks). The basic idea is to have a short bibliography containing vital references and a longer one containing other references that are not vital but may be intersting.

This is not overly difficult using multibib. My main problem is that I would like to have items cited in the main text and in footnotes to be listed only once in the main bibliography.

Here is a pseudo-code of what I would like to have.

\documentclass{article}
% Here a definition of the \citespecial command.
\begin{document}
Some text \cite{a,b} and there a footnote\footnote{\citespecial{b,c,d}}
\bibliographystyle{plain}
\bibliography{mybib}
\end{document} 

The result should have a, b in the main bibliography and c, d in the second one but not b since it already appears in the main bibliography.

I am currently a bibtex user but I can consider using biblatex.

For the record, here is a MWEusing multibib

\documentclass{article}
\usepackage{filecontents,multibib}
\usepackage{multibib}
\newcites{secd}{Secondary References}
\begin{filecontents}{essmult.bib}
@ARTICLE{a,
  author       = "Doe, J.",
  title        = "Title, Part 1",
  journal      = "Interesting Journal 1",
  year         = "1991",
  volume       = "1",
  pages        = "1--11",
}
@ARTICLE{b,
  author       = "Doe, J.",
  title        = "Title, Part 2",
  journal      = "Interesting Journal 2",
  year         = "1992",
  volume       = "2",
  pages        = "2--22",
}
@ARTICLE{c,
  author       = "Doe, J.",
  title        = "Title, Part 3",
  journal      = "Interesting Journal 3",
  year         = "1993",
  volume       = "3",
  pages        = "3--33",
}
@ARTICLE{d,
  author       = "Doe, J.",
  title        = "Title, Part 4 ",
  journal      = "Interesting Journal 4",
  year         = "1993",
  volume       = "4",
  pages        = "4--44",
}
\end{filecontents}
\begin{document}
Some text \cite{a,b} and there a footnote\footnote{\protect\citesecd{b,c,d}}
\bibliographystylesecd{plain}
\bibliographysecd{essmult}
\bibliographystyle{plain}
\bibliography{essmult}
\end{document} 

giving the following result, showing the unfortunate repetition that I am trying to avoid

enter image description here