Ok, if you only have the car in front, make sure that you don't try to make this perfect.
I know what I am saying - this year I had the test for getting a US driver's license.
In Romania the parallel parking is taught differently than here - you are not allowed to adjust your position - you can only go in reverse.
When I had the test in Romania I was able to do a parallel parking with only going in reverse and leaving 50 cm in front of my car and 50 in the back of my car...
Of course I forgot how to do it as after that I had places where I would go in perpendicular to the curb, not parallel...
One week before the US test I got a driving hour in that area to see how it is.
At the end I had to do a parallel parking behind a car, exactly how you say, without another car behind me.
I did it ok.
During the test, when it came to the parallel parking, I tried to do it fine - well, I was going to hit the curb.
As I knew that would mean failing the test, I told the examiner - if I go further back I will hit the curb.
He said: do what you would do if you would be parking in front of your house.
So I exited and tried again. I had to exit as I was too close to the car in front to adjust with back forward moves.
This time it was a little better, but I would have still hit the curb.
Again, he said to do what I would do at home.
As this time I could do back forward, I did that .
So, keep in mind that at the exam if you won't have a car behind you you will be able to start the parking movement a little later than normal.
If you start it later, that means that even if you don't have enough lateral distance you can get away by not turning the steering wheel completely to the right...
That "should" guarantee you will be able to do it, even if you end up at a bigger distance from the car in front than normal.
But, be also aware that trying to adjust the parking is not really working if you don't understand how it works and more if you don't have enough practice.
So my suggestion remains - practice.
Perhaps talk with the instructor to have several sessions only for the maneuvers?
I know my instructor did this - we got to a driving "range" and he told me - you have to do the following "obstacle course" in under 2:30 minutes.
We will do only this until you do it right.
The course was:
0-1-Start from stand still;
1-2-stop uphill, start from uphill;
2-3-front in parking;
3-4-back out from parking;
4-5-slalom;
5-6-parallel parking;
6-7-exit from parking;
7-8-reverse, back in parking;
8-9-exit from parking and the course
I remember having blisters and blood on my hands as the car did not have power steering and the instructor had some rubber things on the steering wheel to increase grip for the students - but the rubber grip had some bumps like the lego bricks have :)
The fine thing was that my instructor first demonstrated it while explaining how to do it and why you should do it that way - he explained what the car does and the physics involved.
Then he told me to stay outside and watch him to be able to understand better.
Then after I tried he would explain what I was doing wrong and how to fix it.