Transparent objects covering each other - graphics

Question

For an academic project I'm trying to write a code for drawing billboards from scratch; now I'm at the point of making them translucent. I've managed to make them look good against the background but they still may cover each other with their should-be-transparent corners, like in this picture:
I'm not sure what I'm doing wrong. This is the effect file I'm using to draw the billboards. I've omitted the parts related to the vertex shader, which I think is irrelevant right now.
//cut
texture Texture;
texture MaskTexture;
sampler Sampler = sampler_state
{
Texture = (Texture);
MinFilter = Linear;
MagFilter = Linear;
MipFilter = Point;
AddressU = Clamp;
AddressV = Clamp;
};
sampler MaskSampler = sampler_state
{
Texture = (MaskTexture);
MinFilter = Linear;
MagFilter = Linear;
MipFilter = Point;
AddressU = Clamp;
AddressV = Clamp;
};
//cut
struct VertexShaderOutput
{
float4 Position : POSITION0;
float4 Color : COLOR;
float2 TexCoord : TEXCOORD0;
};
//cut
float4 PixelShaderFunction(VertexShaderOutput input) : COLOR0
{
float4 result = tex2D(Sampler, input.TexCoord) * input.Color;
float4 mask = tex2D(MaskSampler, input.TexCoord);
float alpha = mask.r;
result.rgb *= alpha;
result.a = alpha;
return result;
}
technique Technique1
{
pass Pass1
{
VertexShader = compile vs_2_0 VertexShaderFunction();
PixelShader = compile ps_2_0 PixelShaderFunction();
AlphaBlendEnable = true;
SrcBlend = SrcAlpha;
DestBlend = InvSrcAlpha;
}
}
I've got two textures, named Texture and MaskTexture, the latter being in grayscale. The billboards are, most likely, in the same vertex buffer and are drawn with a single call of GraphicsDevice.DrawIndexedPrimitives() from XNA.
I've got a feeling I'm not doing the whole thing right.

Answer 1

You have to draw them in order. From farthest to closest.

Answer 2

I have found a solution. The shaders are fine, the problem turned out to be in the XNA code, so sorry for drawing your attention to the wrong thing.
The solution is to enable a depth stencil buffer (whatever it is) before drawing the billboards:
device.DepthStencilState = DepthStencilState.DepthRead;
It can be disabled afterwards:
device.DepthStencilState = DepthStencilState.Default;