Amazon Web Services : Setting S3 policy to allow putObject and getObject but deny listBucket

I am using getObject and putObject requests on Amazon S3 and in creating a policy for access to the bucket I discovered that if I don't allow listBucket I get an 'access denied' error.

The problem with this is that listBucket means a user can list the keys in a bucket and this presents a security threat.

Is it possible to allow getObject and putObject without allowing listBucket? or is there a workaround for this?

Here is the policy:

 {
 "Version": "2012-10-17",
"Statement": [
{
  "Sid": "Stmt##",
  "Effect": "Allow",
  "Action": [
    "s3:ListBucket"
  ],
  "Resource": [
    "arn:aws:s3:::myBucket"
  ]
},
{
  "Sid": "Stmt##",
  "Effect": "Allow",
  "Action": [
    "s3:GetObject",
    "s3:PutObject"
  ],
  "Resource": [
    "arn:aws:s3:::myBucket/*"
  ]
}
 ]
}