When architect Bill Bechhoefer built the addition to his Cape Cod-style home, he rented a house across the street so he could supervise the construction. He was standing outside one day when a neighbor stopped by to gasp at the starkly modern structure going up behind the tiny dormers at the front of the house.

"That your house?" asked the neighbor.

"Yes," replied Bechhoefer proudly.

"You an architect?" asked the older man with a puzzld expression on his face.

"Yes," answered the University of Maryland architecture professor.

The man shook his head, looked up at the addition, then over at the architect.

"It figures," he mumbled, continuing his stroll down the street.

Perhaps only an architect would consider building onto such an unlikely candidate for a modern addition.

"What we did is buy a view," says Bechhoefer, whose home overlooks the C & O Canal and the Potomac River. In fact, the original home could best be described as a foyer. The 3,000-square-foot structure started off as about 800 square feet plus attic.

"I tried to figure out a way to harmonize the old section of the house with the new. I even gave the problem to an advanced design class of mine." recalls the architect. "But in the end almost every design looked compromised, and I decided that if I couldn't marry the two then it was better to be blatant abut it."

The result is a somewhat humorous street-side vision of a tiny traditional home dwarfed by a massive wooden addition. In time Bechhoefer hopes that the wood will gray down and become a background for the old house. Right now, it is controversional structure in the tiny community of Brookmont, Md. It even provoked neighbors to ask Bechhoefer when he planned to tear down the old house in front of the new one.

To take maximum advantage of the view, the architect reoriented the whole house so the living and dining rooms facr the river. The kitchen is essentially in the same place as before, but the orientation is different. The front rooms of the old house now include a study and a guest room.

The Bechhoefers bought their house fully intending to add on. But for most homeowners, the idea o putting on an addition emerges out of necessity. The family has outgrown the house and the prospect of moving is either too costly or the neighborhood too hard to leave.

Last year, according to the U.S. Department of Commerce, homeowners spent $28.3 billion for upkeep and improvement of their homes -- a figure that is 17 percent up from 1978. Of that money, some $20.7 billion went for home improvements -- including $2.6 billion for additions alone. In short, remodeling and adding on are options more and more homeowners are selecting. Professional Remodelling magazine provides the following cost breakdown for a typical custom remodeling of about $24,000: 37 percent for subcontractors 25 percent for materials 21 percent for overhead 10 percent for labor 5 percent for profit 2 percent for permits, plans and equipment.

There are all sorts of possibilities for an addition -- popping up a dormer in the attic, converting a garage or adding a whole new wing. For those considering an addition, local architects estimate that new construction costs run around $50 to $75 per square foot.

Once the financial questions are put aside, homeowners can concentrate on the spaces. Family rooms are much in demand for additions, witness the "lobster room" designed as part of a massive 3,000-square-foot addition by Winthrop Faulkner. The 26-by-26 foot room has a dramatic 18-foot cathedral ceiling and handsome beam work.

Unlike Bechhoefer's, Winthrop Faulkner's addition relates on both interior and exterior spaces to the original house. The truss work in the "lobster room" mirrors and magnifies beams in a small enclosed eating porch in the original house. Here they are magnified many times and create a wonderful rhythm and interplay with the windows on either side of the fireplace.

The old and new wings are connected by a one-story kitchen. Also included in the new wing is a guest bedroom, a maid's room and a laundry, plus a tiny hideaway space on the third level. In the basement, there is a studio and game room for teen-age children.

For the addition on a 1930s modern home in Northwest Washington, a family room or music room and a new master bedroom wing were the main motivations. The original house was designed by Arthur Castner, a well-known Philadelphia architect. The boxy brick house was one of the earliest international-style houses built in the District. The 3,000-square-foot curved-wall addition by Don Lethbridge is in stark contrast to the original home, but at the same time complementary.

The two-story space is separated from the original house by a glass wall which obscures the stairwell. The addition includes a family/music room on the first floor along with a separate guest room and bath. Above, the owners have a completely private wing -- a bedroom overlooking a pool. The wing includes a bathing and dressing corridor with his and hers bathrooms, an exercise corner and lots and lots of closer space.

The overall effect of the addition is to soften the harsh simplicity of the original house through the use of curving walls without making a dramatic break with the style established by the original architect.

Unlike many additions in which the architect acts as an extension of the original designer of the home, in these homes the architects have made dramatic individual statements, creating additions that indeed make a difference.