There are three main ways conflicts between legal effects (obligations, institutional facts, etc.) are derogated.
Lex superior - the effect originating from the highest priority legal source (e.g. human rights charters) derogates.
Lex posterior - the effect originating from the most recently enacted legislation derogates.
Lex specialis - the most specific effect derogates (e.g. any EU product can be sold in any EU country. Italy requires only pasta made from wheat can be sold as pasta. Germany makes pasta made from some other product. Italy's law is more specific and therefore German-labelled pasta which does not constitute pasta to Italy's legal system cannot be sold in Italy).
If a more specialised effect somehow contradicts an effect from a higher source, then one principle must be determined as taking precedent over another. It depends on the legal system which is which. I don't know any legal system where an effect from superior source has been derogated by an inferior source. Human Rights law should always take precedent, so should a constitution, under the lex superior principle.