diff --git a/src/pip/_internal/resolution/resolvelib/found_candidates.py b/src/pip/_internal/resolution/resolvelib/found_candidates.py
index c9b21727a..491290466 100644
--- a/src/pip/_internal/resolution/resolvelib/found_candidates.py
+++ b/src/pip/_internal/resolution/resolvelib/found_candidates.py
@@ -1,89 +1,51 @@
+import functools
+import itertools
+
 from pip._vendor.six.moves import collections_abc  # type: ignore
 
 from pip._internal.utils.compat import lru_cache
 from pip._internal.utils.typing import MYPY_CHECK_RUNNING
 
 if MYPY_CHECK_RUNNING:
-    from typing import Callable, Iterator, Optional, Set
+    from typing import Any, Callable, Iterator, Optional, Set
 
     from pip._vendor.packaging.version import _BaseVersion
 
     from .base import Candidate
 
 
-class _InstalledFirstCandidatesIterator(collections_abc.Iterator):
-    """Iterator for ``FoundCandidates``.
-
-    This iterator is used when the resolver prefers to keep the version of an
-    already-installed package. The already-installed candidate is always
-    returned first. Candidates from index are accessed only when the resolver
-    wants them, and the already-installed version is excluded from them.
-    """
-    def __init__(
-        self,
-        get_others,  # type: Callable[[], Iterator[Candidate]]
-        installed,  # type: Optional[Candidate]
-    ):
-        self._installed = installed
-        self._get_others = get_others
-        self._others = None  # type: Optional[Iterator[Candidate]]
-        self._returned = set()  # type: Set[_BaseVersion]
-
-    def __next__(self):
-        # type: () -> Candidate
-        if self._installed and self._installed.version not in self._returned:
-            self._returned.add(self._installed.version)
-            return self._installed
-        if self._others is None:
-            self._others = self._get_others()
-        cand = next(self._others)
-        while cand.version in self._returned:
-            cand = next(self._others)
-        self._returned.add(cand.version)
-        return cand
-
-    next = __next__  # XXX: Python 2.
+def _deduplicated_by_version(candidates):
+    # type: (Iterator[Candidate]) -> Iterator[Candidate]
+    returned = set()  # type: Set[_BaseVersion]
+    for candidate in candidates:
+        if candidate.version in returned:
+            continue
+        returned.add(candidate.version)
+        yield candidate
 
 
-class _InstalledReplacesCandidatesIterator(collections_abc.Iterator):
+def _replaces_sort_key(installed, candidate):
+    # type: (Candidate, Candidate) -> Any
+    return (candidate.version, candidate is installed)
+
+
+def _insert_installed(installed, others):
+    # type: (Candidate, Iterator[Candidate]) -> Iterator[Candidate]
     """Iterator for ``FoundCandidates``.
 
     This iterator is used when the resolver prefers to upgrade an
     already-installed package. Candidates from index are returned in their
     normal ordering, except replaced when the version is already installed.
+
+    The sort key prefers the installed candidate over candidates of the same
+    version from the index, so it is chosen on de-duplication.
     """
-    def __init__(
-        self,
-        get_others,  # type: Callable[[], Iterator[Candidate]]
-        installed,  # type: Optional[Candidate]
-    ):
-        self._installed = installed
-        self._get_others = get_others
-        self._others = None  # type: Optional[Iterator[Candidate]]
-        self._returned = set()  # type: Set[_BaseVersion]
-
-    def __next__(self):
-        # type: () -> Candidate
-        if self._others is None:
-            self._others = self._get_others()
-        try:
-            cand = next(self._others)
-            while cand.version in self._returned:
-                cand = next(self._others)
-            if self._installed and cand.version == self._installed.version:
-                cand = self._installed
-        except StopIteration:
-            # Return the already-installed candidate as the last item if its
-            # version does not exist on the index.
-            if not self._installed:
-                raise
-            if self._installed.version in self._returned:
-                raise
-            cand = self._installed
-        self._returned.add(cand.version)
-        return cand
-
-    next = __next__  # XXX: Python 2.
+    candidates = sorted(
+        itertools.chain(others, [installed]),
+        key=functools.partial(_replaces_sort_key, installed),
+        reverse=True,
+    )
+    return iter(candidates)
 
 
 class FoundCandidates(collections_abc.Sequence):
@@ -106,22 +68,27 @@ class FoundCandidates(collections_abc.Sequence):
 
     def __getitem__(self, index):
         # type: (int) -> Candidate
-        # Implemented to satisfy the ABC check, This is not needed by the
+        # Implemented to satisfy the ABC check. This is not needed by the
         # resolver, and should not be used by the provider either (for
         # performance reasons).
         raise NotImplementedError("don't do this")
 
     def __iter__(self):
         # type: () -> Iterator[Candidate]
-        if self._prefers_installed:
-            klass = _InstalledFirstCandidatesIterator
+        if not self._installed:
+            candidates = self._get_others()
+        elif self._prefers_installed:
+            candidates = itertools.chain([self._installed], self._get_others())
         else:
-            klass = _InstalledReplacesCandidatesIterator
-        return klass(self._get_others, self._installed)
+            candidates = _insert_installed(self._installed, self._get_others())
+        return _deduplicated_by_version(candidates)
 
     @lru_cache(maxsize=1)
     def __len__(self):
         # type: () -> int
+        # Implement to satisfy the ABC check and used in tests. This is not
+        # needed by the resolver, and should not be used by the provider either
+        # (for performance reasons).
         return sum(1 for _ in self)
 
     @lru_cache(maxsize=1)