Disabling direct creation allowing creation only via NEW and smart pointer

This is an experiment to see if it can be done.

By making destructor private, I'm able to disable direct object creation (ex: Test t; ). I want to force instantiation via new (this works) or smart pointer like unique_ptr.

I believe that I'm doing something wrong with how I'm approaching unique_ptr but I'm not sure what.

#include<iostream>
#include<string>
#include<memory>
using namespace std;

class Test
{
private:
    ~Test() {cout << "x" << endl;}
public:
    Test() {cout << "c" << endl;}
    static void destruct(Test* ptr) {delete ptr;}
};

int main()
{
    //Perfect
    //We want to disable direct creation. This fails and we want it to fail.
    //Test t;  ERROR: Can't because dest is private!

    //OK   
    Test *ptr = new Test;       //Creation via new works fine
    ptr->destruct(ptr);         //Destruct works fine

    //NOT OK. :-(
    //auto up = make_unique<Test>();  //error
    //unique_ptr<Test> up( new Test(), [](Test* p){destruct(p);} );     //error

    return 0;
}