Dissolve Lines without Dissolving Convergent Lines?

Question

I've been playing with arcHydro and related processes a bit and have run into an obstacle. I have been creating stream networks from the flow accumulation, direction, and stream order functions. When converted from raster to polygon each segment of the streams is a unique feature within the output feature class. I would like it so that if there is no change in order from one segment to the next, that it is the same feature. Easy enough, dissolve.

The issue now is that where two streams of the same order come together to form a stream of a greater order, the two smaller order streams dissolve into 'one' stream as they share a vertex (their shared outlet which is the inlet of the greater order stream subsequent). Difficult to describe without visuals but I'm hoping this was clear.

EDIT I'm attaching some visuals to help clarify.

The first image is the layer as it converts from raster; with each line segment being it's own feature.

The second image is following a dissolve. The 'conflict' areas are those circled in red, where a common vertice has caused two streams of the same order to dissolve together when in fact they only share an outlet. For my purposes, I don't want this to be the case. Hoping the visuals help clarify.

Answer 1

I have come up with an approach:

1. Create a point layer with points for each vertex in the stream network layer
2. Buffer each vertex a (small) desired amount (I arbitrarily chose 10 metres)
3. Run intersect and create points as the output, this will create a series of points where the buffer intersects the stream layer at the setback amount.
4. Identify which points of intersection are of the desired order or greater. Remove those that are not.
5. Identify the smallest remaining order within the buffer. Any points greater than the smallest order (i.e the stream being flowed into) will be removed.
6. Left with the smallest order points which are greater than the specified minimum order of concern.
7. These are the pour points (automated). I snapped the pour points back half of the original setback (5m). So the pour point should be 5 or so metres from the actual outlet (dependent on the shape of the stream), which makes for clean delineation.

Hoping the brief description is clear.