How can I improve that first cold contact with a potential client?

Sharpen your focus and target small groups of people you are confident you can contribute to most.

Your existing (best) customers will provide the clarity you need to establish this.  Less is more, work in a narrow pipe and leverage each call by communicating with benefits, specialised knowledge and commonality - this helps build rapport and develops foundations of trust.

Cold-calling is as much about process, support and leverage as it is about dealing with rejection and maintaining enthusiasm. You have to work to a structured plan and initiative contact as you would a warm referral, i.e. I know who you and your competitors are - and the reason for my call is to help you, just like I have helped others in your space.  

I often indulge cold-callers simply because I'm curious to learn what they say and how they engage customers.  I recommend any cold-caller do the same to pick up valuable insights. Recently, I asked a cold-caller who randomly contacted me, what the nature of my business was? His response, "Um, could you please give me your web address?"  Clearly he did not care about me or my business, nor had he taken the time to buy-in and demonstrate an interest in my best interests.

Traditional cold-calling is about volume and working with the law of averages. Contrastingly, modern cold-calling is more about understanding your niche and carving-a-path to market that engages customers in meaningful conversations and leads them (willingly) to benefits via your sales-process.