This well-maintained park has a fenced area for small dogs

 The dog park is 1.25 acres in size, cross fenced for separate big dog and small dog play areas.
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Off-leash dog recreation area, trails for hiking but not completely fenced, except for a small grassy area at the bottom. Hiking the main, paved trail, top to bottom, takes a little over an hour. There are two dirt trails that stretch top to bottom as well, one on either crest, with the paved path winding up the floor of the canyon. Lots of dogs and people at all times. Water fountains for dogs only at the bottom. Top parking lot/entrance: Mullholland Drive, about five minutes west of the 101. Bottom parking/entrance: street parking, entrance is at north end of Fuller Ave.
The park includes an all-season area, as well as separate fenced areas for large and small dogs.
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In an apartment or condominium, the real difficulty is likely to be that there is no yard of any kind. Many such situations have little or no vacant land belonging to the building, and such land if any is subject to the use of all the tenants or owners. If there is an adequate amount of common ground, and if there are a fair number of dog-owners in the building, you might consider organizing together to ask the landlord or the Owner's Association if some small portion of the common land might be fenced in (paid for by the dog owners as a group) to serve as the dog "exercise", ie elimination, area. If all the dog owners were to agree to confine their pets' eliminations to this area and to scoop up immediately into an appropriate container or dog-septic repository, then all tenants would enjoy the benefits of the remainder of the common areas being kept squeeky clean. If you can't get a dog yard, then at least make friends with some or all of the other dog owners and make some mutual aid agreements to walk each others dogs in the event of illness or other problems. It's important to educate all dog owners to the absolute necessity of scooping up all dog waste on all the common areas, so the building will continue to welcome dogs. There are large, fenced-in play areas for both large and small dogs at Laurel Canyon. Photo.
Photo provided by FlickrFeatures: Large turf area, one-acre site, trash cans, seating area, water for dogs. Small and large dog fenced and lighted areas.
Photo provided by FlickrThis fence system is an easy inexpensive solution for a small area and small dogs, but I do not think it would work for a very large dog. ...
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The toilet function can be satisfied in a very small area. If you have a patio or a tiny little yard, as little as 4 ft X 6 ft or (preferably) 6 X 10 ft (the size of many kennel runs), your dog can relieve himself comfortably. If this yard communicates with your house by a dog-door, so much the better as then the dog can use it whenever he needs to, without asking you to let him out. For male dogs, the addition of a small shrub or a post as target for leg-lifting will be much appreciated. Of course if your yard is this tiny, then you do have to be willing to scoop up (and, if paved, hose off) quite often. If you live on an upper floor apartment or condo, a small balcony can be used as a toilet yard if and only if it is fenced/barricaded in a way that absolutely prevents the dog from jumping off or falling off, consequences of which would be crippling or fatal. We actually have this fence for our backyard. It works very well and looks really nice too. This fence is great for keeping dogs and small livestock in certain areas.Throughout Europe, for centuries, walls were the most common fences. However, Americans were used to vast plains and developed the fabric fence to minimize interference with the wide open spaces. Most fencing is rather expensive, so don't be shy about fencing a small area for the dog even if your yard is huge. Emphasize length; a dog run 10 feet wide and as long as possible in your yard allows the dog to run up and down and exercise nicely.There are other ways small dogs can get into mischief, of course. For them, it’s easy to escape by simply digging holes with their little legs and wriggling their little dog bodies through them. Dachshunds love digging, as do terriers—burrowing in order to hunt small prey is part of their nature. It may be necessary to bury chicken wire under your fence to prevent their escape. If there are particular spots where your dog likes to dig, you also might consider placing large stones in those areas.