We can bring mixed-in methods to the desired overload set, but not operators or constructors. Here's what I mean:

mixin template methodMix()
{
    void foo(int n) { }
}

mixin template operatorMix()
{
    void opBinary(string op)(int n) { }
}

mixin template ctorMix()
{
    this(int n) { }
}

struct MethodTest
{
    mixin methodMix mix;

    alias foo = mix.foo;

    void foo(string s) { }
}

struct OperatorTest
{
    mixin operatorMix mix;

    alias opBinary = mix.opBinary;

    void opBinary(string op)(string s) { } // [1]
}

struct CtorTest
{
    mixin ctorMix mix;

    // If only I could do the following to bring the
    // mixed-in constructor to the overload set:
    //alias this = mix.this;

    this(string s) { }
}

void main()
{
    MethodTest mt;
    mt.foo(3);

    OperatorTest ot;
    ot + 3;

    auto ct = CtorTest(3); // [2]
}
-----------------
1. Error: template test.OperatorTest.opBinary(string op)(string s) conflicts with alias test.OperatorTest.opBinary
2. Error: constructor test.CtorTest.this (string s) is not callable using argument types (int)

Filed an enhancement request:
https://d.puremagic.com/issues/show_bug.cgi?id=11500

On Monday, 11 November 2013 at 21:58:44 UTC, Tommi wrote:
> Filed an enhancement request:
> https://d.puremagic.com/issues/show_bug.cgi?id=11500

Everything should work the same way.

On Tuesday, 12 November 2013 at 01:17:20 UTC, deadalnix wrote:
> On Monday, 11 November 2013 at 21:58:44 UTC, Tommi wrote:
>> Filed an enhancement request:
>> https://d.puremagic.com/issues/show_bug.cgi?id=11500
>
> Everything should work the same way.

Do you mean that what I'm reporting is a compiler-bug rather than a feature request?

On 11/19/2013 11:13 AM, Tommi wrote:
> On Tuesday, 12 November 2013 at 01:17:20 UTC, deadalnix wrote:
>> On Monday, 11 November 2013 at 21:58:44 UTC, Tommi wrote:
>>> Filed an enhancement request:
>>> https://d.puremagic.com/issues/show_bug.cgi?id=11500
>>
>> Everything should work the same way.
>
> Do you mean that what I'm reporting is a compiler-bug rather than a
> feature request?

I'd argue yes, but similar issues have surprisingly attracted some controversy in the past. (The constructor aliasing is an enhancement though as it extends the language grammar.)

On Tuesday, 19 November 2013 at 22:51:10 UTC, Timon Gehr wrote:
> On 11/19/2013 11:13 AM, Tommi wrote:
>> On Tuesday, 12 November 2013 at 01:17:20 UTC, deadalnix wrote:
>>> On Monday, 11 November 2013 at 21:58:44 UTC, Tommi wrote:
>>>> Filed an enhancement request:
>>>> https://d.puremagic.com/issues/show_bug.cgi?id=11500
>>>
>>> Everything should work the same way.
>>
>> Do you mean that what I'm reporting is a compiler-bug rather than a
>> feature request?
>
> I'd argue yes, but similar issues have surprisingly attracted some controversy in the past. (The constructor aliasing is an enhancement though as it extends the language grammar.)

Hmmm... decisions decisions. I changed it from enhancement to bug (normal priority) anyway.