John Davenant writes in his A Dissertation on the Death of Christ (underlining mine):
“Lastly, our own Divines, who do not deny that Christ suffered for all, yet at the same time profess that he redeemed the elect by his death in some peculiar manner. Bucer expresses his opinion on these words (Matt. i. 21)
‘He shall save his people, that is, the elect, whom the Father brings to him. By his death he expiated the sins of all the elect, and merited that the Father being propitious to them should give them his Spirit.’  –CD]
Here observe that Christ by his death merited something for the elect, which he did not merit for others: But what Christ merited for any one, he merited according to the appointment and acceptance of his Father: Therefore, according to the will and appointment of the Father, the death of Christ pertains to the elect in some special way, in which it is not extended to others. …
Zanchius (in Miscell. tract. de praed. Sanct. p. 14) observes,
‘It is not false that Christ died for all men: for the passion of Christ is offered to all in the Gospel. But he died effectually for the elect alone, because indeed they only are made partakers of the efficacy of the passion of Christ.’
But that they only are made partakers effectually of this passion, is to be referred to the special and effectual will of Christ in suffering, and of God the Father in accepting this sacrifice in a peculiar way for the elect more than for others: for in the participation of saving good, the will of God precedes the human will. …
For if it should be inquired, why Peter rather than Judas received effectual grace and salvation from the merit of the death of Christ? it will be answered, according to our opinion, Because Christ, by his special intention, and by the application of his merits, merited that for Peter which he did not merit for Judas. …
Therefore, let this be the sum and conclusion of this whole controversy on the death of Christ; That Jesus Christ, the Mediator between God and man, in confirming the evangelical covenant, according to the tenor of which eternal life is due to everyone that believeth, made no division or separation of men, so that we can say that any one is excluded from the benefit of his death, if he should believe.
And in this sense we contend, in agreement with the Scriptures, the fathers, and solid arguments, that Christ suffered on the cross and died for all men, or for the whole human race. We add, moreover, that this Mediator, when he had determined to lay down his life for sin, had also this special intention, that, by virtue of his merits, he would effectually and infallibly quicken and bring to eternal life, some persons who were specially given to him by the Father. And in this sense we contend that Christ laid down his life for the elect alone, or in order to purchase his Church; that is, that he died for them alone, with the special and certain purpose of effectually regenerating and saving by the merit of his death.
Therefore, although the merit of Christ equally regards all men as to its sufficiency, yet it does not as to its efficacy: which is to be understood, not only on account of the effect produced in one and not in another, but also on account of the will, with which Christ himself merited, and offered his merits, in a different way for different persons.
Now, the first cause and source of this diversity was the election and will of God, to which the human will of Christ conformed itself.” (John Davenant, A Dissertation on the Death of Christ, pp. 547-548, 550, 556-557)
My NOTE:  — CD] G. Michael Thomas writes that Martin Bucer (1491-1551) believed that Christ died only for the elect while also calling “upon all people to believe in their election. This appears to be a logically inconsistent procedure, in that it amounted to requiring people to believe something that was not necessarily true in every case. At the same time, within Bucer’s own terms of reference, it had an experiential consistency, in that no-one [sic] who actually believed in his own election would be believing a falsehood, for such faith could only come as a gift from God, in accordance with his electing will” (G. Michael Thomas, The Extent of the Atonement, p. 7; underlining mine).
Reading John Davenant here calls to my mind what a precious brother in the Lord spoke on at least one occasion:
“The LIE is more complicated than the TRUTH.”
Quite true. There are certain men who dismiss stuff like this with a wave of their high Calvinist hand, saying that Davenant “doesn’t count” since he’s not a “true Calvinist” (whatever that might mean). I am unsure what the high Calvinist response or explanation might be of Davenant’s quote of Jerome Zanchius.
A common dismissal of Davenant is that he is an “Amyraldian.” I think this is an inaccurate description. I believe that John Davenant is actually a “moderate Calvinist” (of the “English hypothetical universalist” variety) and thus an important figure in the damnable Reformed Tradition.
The Reformed Tradition is quite diverse; it is massive and multi-colored. Many and variegated are its explanatory shades of salvation conditioned on the “spiritually-and-infallibly-enabled” efforts of the sinner INSTEAD OF ON THE EFFICACIOUS EFFORTS OF JESUS CHRIST ALONE.
Here is R.L. Dabney teaching the damnable heresy that Jesus Christ made penal satisfaction for everyone without exception (presumably, Dabney “does count” and thus cannot be dismissed as Davenant above):
“Nor would we attach any force to the argument, that if Christ made penal satisfaction for the sins of all, justice would forbid any to be punished. To urge this argument surrenders virtually the very ground on which the first Socinian objection was refuted, and is incompatible with the facts that God chastises justified believers, and holds elect unbelievers subject to wrath till they believe. Christ’s satisfaction is not a pecuniary equivalent, but only such a one as enables the Father, consistently with His attributes, to pardon, if in His mercy He sees fit. The whole avails of the satisfaction to a given man is suspended on his belief. There would be no injustice to the man, if he remaining an unbeliever, his guilt were punished twice over, first in his Savior, and then in him” (R.L. Dabney, Lectures on Systematic Theology, p. 521; underlining mine).
The God-hating Arminians believe that Christ died sufficiently for all, but God-hating Calvinists like Davenant, Dabney, and Zanchius “go further” by saying that there is ALSO a “special reference” to the elect. They would say that Christ died sufficiently for all, but only efficiently for the elect. This is classic Reformed “soteriology.” The Arminians deny the Reformed “special reference” while most (certainly not all ) Calvinists affirm it. In view of this one may perceive that the Reformed Tradition is pretty broad and not quite so discontinuous with Arminianism as one might suspect. They have more in common than people think. [An important note: true believers who call themselves Calvinists should realize that they are not genuine historical Calvinists, and thus should not call themselves Calvinists.]
 If one believes that Jesus Christ died ONLY for the elect and IN NO SENSE for the non-elect, then what sense would it make to speak of a “special reference” when that is the ONLY reference?
“Admitting, however, that the Augustinian doctrine that Christ died specially for his own people does account for the general offer of the gospel, how can it be reconciled with those passages which, in one form or another, teach that He died for all men? In answer to this question, it may be remarked in the first place that Augustinians do not deny that Christ died for all men. What they deny is that He died equally, and with the same design, for all men” (Charles Hodge, Systematic Theology, Volume 2, p. 558).