diff --git a/dvc/dependency/repo.py b/dvc/dependency/repo.py
index 68cd044a1..20439c024 100644
--- a/dvc/dependency/repo.py
+++ b/dvc/dependency/repo.py
@@ -49,10 +49,10 @@ class DependencyREPO(DependencyLOCAL):
 
     def status(self):
         with self._make_repo() as repo:
-            current = repo.find_out_by_path(self.def_path).info
+            current = repo.find_out_by_relpath(self.def_path).info
 
         with self._make_repo(rev_lock=None) as repo:
-            updated = repo.find_out_by_path(self.def_path).info
+            updated = repo.find_out_by_relpath(self.def_path).info
 
         if current != updated:
             return {str(self): "update available"}
@@ -71,7 +71,7 @@ class DependencyREPO(DependencyLOCAL):
         ) as repo:
             self.def_repo[self.PARAM_REV_LOCK] = repo.scm.get_rev()
 
-            out = repo.find_out_by_path(self.def_path)
+            out = repo.find_out_by_relpath(self.def_path)
             with repo.state:
                 repo.cloud.pull(out.get_used_cache())
 
diff --git a/dvc/exceptions.py b/dvc/exceptions.py
index 369b33ac7..ce30ffa88 100644
--- a/dvc/exceptions.py
+++ b/dvc/exceptions.py
@@ -61,10 +61,9 @@ class OutputNotFoundError(DvcException):
 
     def __init__(self, output, repo=None):
         self.repo = repo
-        self.failed_output = output
         super(OutputNotFoundError, self).__init__(
             "unable to find DVC-file with output '{path}'".format(
-                path=relpath(self.failed_output)
+                path=relpath(output)
             )
         )
 
@@ -343,9 +342,7 @@ class RemoteNotSpecifiedInExternalRepoError(DvcException):
 
 
 class NoOutputInExternalRepoError(DvcException):
-    def __init__(self, repo_url, path):
+    def __init__(self):
         super(NoOutputInExternalRepoError, self).__init__(
-            "Output '{}' not found in target repository: '{}'".format(
-                path, repo_url
-            )
+            "Output not found in target repository."
         )
diff --git a/dvc/external_repo.py b/dvc/external_repo.py
index d528af6a5..e86c02926 100644
--- a/dvc/external_repo.py
+++ b/dvc/external_repo.py
@@ -29,7 +29,7 @@ def external_repo(url=None, rev=None, rev_lock=None, cache_dir=None):
         raise RemoteNotSpecifiedInExternalRepoError(url, cause=exc)
     except OutputNotFoundError as exc:
         if exc.repo is repo:
-            raise NoOutputInExternalRepoError(url, exc.failed_output)
+            raise NoOutputInExternalRepoError()
         raise
     repo.close()
 
diff --git a/dvc/repo/__init__.py b/dvc/repo/__init__.py
index 86d6a343c..9f6284ef4 100644
--- a/dvc/repo/__init__.py
+++ b/dvc/repo/__init__.py
@@ -418,13 +418,10 @@ class Repo(object):
         return get_stages(self.graph)
 
     def find_outs_by_path(self, path, outs=None, recursive=False):
-        abs_path = (
-            path if os.path.isabs(path) else os.path.join(self.root_dir, path)
-        )
-
         if not outs:
             outs = [out for stage in self.stages for out in stage.outs]
 
+        abs_path = os.path.abspath(path)
         is_dir = self.tree.isdir(abs_path)
 
         def func(out):
@@ -438,15 +435,12 @@ class Repo(object):
 
         matched = list(filter(func, outs))
         if not matched:
-            if abs_path.startswith(self.root_dir):
-                failed_output = relpath(abs_path)
-            else:
-                failed_output = path
-            raise OutputNotFoundError(failed_output, self)
+            raise OutputNotFoundError(path, self)
 
         return matched
 
-    def find_out_by_path(self, path):
+    def find_out_by_relpath(self, relpath):
+        path = os.path.join(self.root_dir, relpath)
         out, = self.find_outs_by_path(path)
         return out
 
diff --git a/dvc/repo/fetch.py b/dvc/repo/fetch.py
index 0440dddae..531fd4d53 100644
--- a/dvc/repo/fetch.py
+++ b/dvc/repo/fetch.py
@@ -81,7 +81,7 @@ def _fetch_external(self, repo_url, repo_rev, files):
                 cache = NamedCache()
                 for name in files:
                     try:
-                        out = repo.find_out_by_path(name)
+                        out = repo.find_out_by_relpath(name)
                     except OutputNotFoundError:
                         failed += 1
                         logger.exception(
diff --git a/dvc/repo/get.py b/dvc/repo/get.py
index 64ca5eaf0..21d01ed7e 100644
--- a/dvc/repo/get.py
+++ b/dvc/repo/get.py
@@ -49,7 +49,7 @@ def get(url, path, out=None, rev=None):
             # the same cache file might be used a few times in a directory.
             repo.cache.local.cache_types = ["reflink", "hardlink", "copy"]
 
-            o = repo.find_out_by_path(path)
+            o = repo.find_out_by_relpath(path)
             with repo.state:
                 repo.cloud.pull(o.get_used_cache())
             o.path_info = PathInfo(os.path.abspath(out))
diff --git a/tests/func/test_import.py b/tests/func/test_import.py
index 06e8f8c83..067d5be8e 100644
--- a/tests/func/test_import.py
+++ b/tests/func/test_import.py
@@ -8,7 +8,7 @@ import pytest
 from mock import patch
 
 from dvc.config import Config
-from dvc.exceptions import DownloadError
+from dvc.exceptions import DownloadError, NoOutputInExternalRepoError
 from dvc.stage import Stage
 from dvc.system import System
 from dvc.utils import makedirs
@@ -154,3 +154,8 @@ def test_pull_non_workspace(git, dvc_repo, erepo):
     os.remove(stage.outs[0].cache_path)
     dvc_repo.fetch(all_tags=True)
     assert os.path.exists(stage.outs[0].cache_path)
+
+
+def test_import_non_existing(dvc_repo, erepo):
+    with pytest.raises(NoOutputInExternalRepoError):
+        dvc_repo.imp(erepo.root_dir, "invalid_output")