diff --git a/go/enclave/enclave.go b/go/enclave/enclave.go
index 0e7b1993bd..64a4ddd652 100644
--- a/go/enclave/enclave.go
+++ b/go/enclave/enclave.go
@@ -1252,6 +1252,12 @@ func (e *enclaveImpl) DoEstimateGas(args *gethapi.TransactionArgs, blkNumber *ge
 	// Execute the binary search and hone in on an isGasEnough gas limit
 	for lo+1 < hi {
 		mid := (hi + lo) / 2
+		if mid > lo*2 {
+			// Most txs don't need much higher gas limit than their gas used, and most txs don't
+			// require near the full block limit of gas, so the selection of where to bisect the
+			// range here is skewed to favor the low side.
+			mid = lo * 2
+		}
 		failed, _, err := e.isGasEnough(args, mid, blkNumber)
 		// If the error is not nil(consensus error), it means the provided message
 		// call or transaction will never be accepted no matter how much gas it is