As far as I know, unless a contract/compact states otherwise, or a provision was added at a different point of time, every provision in the contract carries the same priority. The bill of rights was added to the constitution all at once and so each amendment carries the same priority and so when there is a conflict least restrictive means has to be applied.
Sometimes rights conflict with each other, and the courts decide which right takes priority.
The Sixth Amendment provides that a defendant is entitled to "compulsory process for obtaining witnesses in his favor". The Fifth Amendment says "No person... shall be compelled in any criminal case to be a witness against himself". And the First Amendment gives the right to free speech, which includes the right to not be compelled to speak.
If you're on trial and try to get someone else to confess on the stand, his Fifth Amendment right against self-incrimination trumps your Sixth Amendment right to have him testify. But if he couldn't take the fifth (for example, if he had already been acquitted), your Sixth Amendment right would override his First Amendment right to free speech.