A random hat is given when you join the game. However, it's out of place on the characters head?

Hello, I created a script that randomizes skin color, hair, and face, when you join the game. I managed to do all this, however, the hat is out of place. I tried everything to fix it and I'm having no luck.

--Hats
local HairAttachment = Instance.new("Attachment")
HairAttachment.Name = "HairAttachment"
HairAttachment.Parent = Hat1Mesh
local Acessory = Instance.new("Accessory")
Acessory.Name = "Hair"
Acessory.Parent = player.Character

if HatChance == 1 then
    Hat1Mesh.Parent = Acessory
    Hat1Mesh.Name = "Handle"
elseif HatChance == 2 then
    Hat2Mesh.Parent = Acessory
    Hat2Mesh.Name = "Handle"
elseif HatChance == 3 then
    Hat3Mesh.Parent = Acessory
    Hat3Mesh.Name = "Handle"
end