The Trigger Effect.
We've known shooters who boast about very light pulls (sometimes adjusted by themselves, sometimes by gunsmiths). They get a light pull by reducing sear engagement to a bare minimum. Then they have to close the bolt carefully so the sear will hold. Occasionally, if the safety is engaged and then released, the sear will release at the same time.
Our armorer friend demands absolute reliability, even if it's extremely hot or cold, if the mechanism is oily or dusty, if the bolt is worked vigorously or the gun is accidentally dropped. He says that the 700 trigger (which he considers one of the best factory triggers available) is simply not intended or designed for a really light pull.
When a light pull is required, the armorer installs a Jewell match-grade trigger. Jewell triggers are a favorite with benchrest shooters, and they are made like Swiss watches. They are designed specifically to be safe and reliable at light weights of pull. Working parts are made of 440C stainless steel and hardened to 58 Rockwell C (which is very hard indeed) for durability.
The model you want is the Jewel H-VR (hunting-varmint). It comes fitted with a standard spring, adjustable over a weight range of 1/2 to 1/4 lb. Two extra springs included can provide a range of 2.5 oz. to 16 oz. or 1.5 oz. to 5 oz. For hunting, there is little need for the lighter springs. Light triggers take some getting used to, so keep the weight at a level you can handle with complete safety.
Speaking of safety, the Jewell trigger is available with the safety lever either on top or bottom, left or right side. It's a remarkable unit with just two faults: it's not cheap, and it is currently available only for the Winchester 70, Remington 700, custom benchrest actions (i.e. Hart, Stolle, Shilen, Hall, Wichita) and AR-15 rifles.