A lot of companies have reduced staff numbers so that they can save money. (in order to)
A lot of companies have reduced staff numbers in order to save money.
They had to leave the hotel early. If they hadn't, they would have missed their train. (so that)
They had to leave the hotel early so that they wouldn't miss their train.
She didn't get the job in spite of being a strong candidate. (though)
he didn't get the job, though she was a strong candidate. / She didn't get the job. She was a strong candidate, though.
I bought the shoes in spite of the fact that they were ridiculously expensive. (even though)
I bought the shoes even though they were ridiculously expensive.
Even though the flight was long, she felt great when she arrived in New York. (despite)
Despite the long flight / Despite the fact the flight was long, she felt great when she arrived in New York.
In spite of the cold weather, the barbecue was a success. (although)
Although the weather was cold, the barbecue was a success.
Nick didn't tell Louisa the truth because he didn't want to hurt her feelings. (so as)
Nick didn't tell Louisa the truth so as not to hurt her feelings.
The company has a big market share even though they do very little advertising. (in spite of)
The company has a big market share in spite of doing very little advertising / in spite of the fact that they do very little advertising.