While things were better for the Confederates with the Harriet Lane removed from the Union's arsenal, the shore batteries were still undermatched with the U.S Navy's remaining guns. The Neptune was sunk and no longer available. Moreover, the Confederates also soon realized the Buffalo Bayou was stuck so fast to the Harriet Lane, it could not effectively be maneuvered. This was not known by the Union forces. Nevertheless, the situation did not look good for the Confederates.
Detail of a contemporary drawing of the Bayou City and the Harriet Lane the drawing was made by George Grover and is located in the Rosenberg Library, Galveston, Texas
This drawing by Emil Bruje shows the Neptune grounded off to the right and the Owasco coming up from the left while the Harriet Lane and Bayou City are joined
Leon Smith in command aboard the Harriet Lane, decided on a bluff. He raised the white flag from the Harriet Lane and asked for a parley. The Union officers agreed because they wanted to evaluate the condition of the Harriet Lane and because one their ships, the Westfield, had run aground. The parley would buy them time to attempt to work on both problems.
This is from another drawing provided by the Rosenberg Library and shows the position of all ships as of 6:30 AM as drawn by Union artist James E. Bourke in a boat located in the middle of the drawing on January 1, 1863. The labels are mine.