Push down firmly to a depth of 5\u20136cm \u2014 roughly a third of the depth of the chest. This sounds deep but is necessary to actually compress the heart and pump blood. Light or shallow compressions do not move enough blood to be effective.
Allow the chest to fully recoil (rise back up) between each compression. Leaning on the chest prevents the heart from refilling between compressions.
If you are worried about causing injury, it is worth knowing that rib fractures do sometimes occur during effective CPR \u2014 particularly in older adults. A broken rib is a treatable injury. Cardiac arrest without CPR is not survivable. Effective CPR is always worth any risk of minor injury.