diff --git a/stdlib/public/core/Filter.swift.gyb b/stdlib/public/core/Filter.swift.gyb
index 7f12d20d60ee0..5b3cec6cd597a 100644
--- a/stdlib/public/core/Filter.swift.gyb
+++ b/stdlib/public/core/Filter.swift.gyb
@@ -97,65 +97,8 @@ public struct LazyFilterSequence<Base : Sequence>
 }
 
 /// The `Index` used for subscripting a `LazyFilterCollection`.
-///
-/// The positions of a `LazyFilterIndex` correspond to those positions
-/// `p` in its underlying collection `c` such that `c[p]`
-/// satisfies the predicate with which the `LazyFilterIndex` was
-/// initialized.
-///
-/// - Note: The performance of advancing a `LazyFilterIndex`
-///   depends on how sparsely the filtering predicate is satisfied,
-///   and may not offer the usual performance given by models of
-///   `Collection`.
-public struct LazyFilterIndex<Base : Collection> {
-
-  /// The position corresponding to `self` in the underlying collection.
-  public let base: Base.Index
-}
-
-extension LazyFilterIndex : Comparable {
-  public static func == (
-    lhs: LazyFilterIndex<Base>,
-    rhs: LazyFilterIndex<Base>
-  ) -> Bool {
-    return lhs.base == rhs.base
-  }
-
-  public static func != (
-    lhs: LazyFilterIndex<Base>,
-    rhs: LazyFilterIndex<Base>
-  ) -> Bool {
-    return lhs.base != rhs.base
-  }
-
-  public static func < (
-    lhs: LazyFilterIndex<Base>,
-    rhs: LazyFilterIndex<Base>
-  ) -> Bool {
-    return lhs.base < rhs.base
-  }
-
-  public static func <= (
-    lhs: LazyFilterIndex<Base>,
-    rhs: LazyFilterIndex<Base>
-  ) -> Bool {
-    return lhs.base <= rhs.base
-  }
-
-  public static func >= (
-    lhs: LazyFilterIndex<Base>,
-    rhs: LazyFilterIndex<Base>
-  ) -> Bool {
-    return lhs.base >= rhs.base
-  }
-
-  public static func > (
-    lhs: LazyFilterIndex<Base>,
-    rhs: LazyFilterIndex<Base>
-  ) -> Bool {
-    return lhs.base > rhs.base
-  }
-}
+@available(swift, deprecated: 3.1, obsoleted: 4.0, message: "Use Base.Index")
+public typealias LazyFilterIndex<Base : Collection> = Base.Index
 
 // FIXME(ABI)#27 (Conditional Conformance): `LazyFilter*Collection` types should be
 // collapsed into one `LazyFilterCollection` using conditional conformances.
@@ -170,20 +113,23 @@ extension LazyFilterIndex : Comparable {
 /// underlying collection that satisfy a predicate.
 ///
 /// - Note: The performance of accessing `startIndex`, `first`, any methods
-///   that depend on `startIndex`, or of advancing a `LazyFilterIndex` depends
+///   that depend on `startIndex`, or of advancing an index depends
 ///   on how sparsely the filtering predicate is satisfied, and may not offer
 ///   the usual performance given by `Collection`. Be aware, therefore, that
 ///   general operations on `LazyFilterCollection` instances may not have the
 ///   documented complexity.
 public struct ${Self}<
   Base : ${collectionForTraversal(Traversal)}
-> : LazyCollectionProtocol, ${collectionForTraversal(Traversal)} {
+> : LazyCollectionProtocol, ${collectionForTraversal(Traversal)}
+// FIXME(ABI): Recursive protocol conformances
+  where Base.SubSequence: ${collectionForTraversal(Traversal)}
+{
 
   /// A type that represents a valid position in the collection.
   ///
   /// Valid indices consist of the position of every element and a
   /// "past the end" position that's not valid for use as a subscript.
-  public typealias Index = LazyFilterIndex<Base>
+  public typealias Index = Base.Index
 
   public typealias IndexDistance = Base.IndexDistance
 
@@ -209,7 +155,7 @@ public struct ${Self}<
     while index != _base.endIndex && !_predicate(_base[index]) {
       _base.formIndex(after: &index)
     }
-    return LazyFilterIndex(base: index)
+    return index
   }
 
   /// The collection's "past the end" position---that is, the position one
@@ -218,7 +164,7 @@ public struct ${Self}<
   /// `endIndex` is always reachable from `startIndex` by zero or more
   /// applications of `index(after:)`.
   public var endIndex: Index {
-    return LazyFilterIndex(base: _base.endIndex)
+    return _base.endIndex
   }
 
   // TODO: swift-3-indexing-model - add docs
@@ -230,12 +176,12 @@ public struct ${Self}<
 
   public func formIndex(after i: inout Index) {
     // TODO: swift-3-indexing-model: _failEarlyRangeCheck i?
-    var index = i.base
+    var index = i
     _precondition(index != _base.endIndex, "can't advance past endIndex")
     repeat {
       _base.formIndex(after: &index)
     } while index != _base.endIndex && !_predicate(_base[index])
-    i = LazyFilterIndex(base: index)
+    i = index
   }
 
 %   if Traversal == 'Bidirectional':
@@ -247,12 +193,12 @@ public struct ${Self}<
 
   public func formIndex(before i: inout Index) {
     // TODO: swift-3-indexing-model: _failEarlyRangeCheck i?
-    var index = i.base
+    var index = i
     _precondition(index != _base.startIndex, "can't retreat before startIndex")
     repeat {
       _base.formIndex(before: &index)
     } while !_predicate(_base[index])
-    i = LazyFilterIndex(base: index)
+    i = index
   }
 %   end
 
@@ -261,22 +207,14 @@ public struct ${Self}<
   /// - Precondition: `position` is a valid position in `self` and
   /// `position != endIndex`.
   public subscript(position: Index) -> Base.Iterator.Element {
-    return _base[position.base]
+    return _base[position]
   }
 
-  public subscript(bounds: Range<Index>) -> ${Slice}<${Self}<Base>> {
-    return ${Slice}(base: self, bounds: bounds)
+  public subscript(bounds: Range<Index>) -> ${Self}<Base.SubSequence> {
+    return ${Self}<Base.SubSequence>(_base: _base[bounds], _predicate)
   }
 
-  // FIXME(ABI)#28 (Associated Types with where clauses): we actually want to add:
-  //
-  //   typealias SubSequence = ${Self}<Base.SubSequence>
-  //
-  // so that all slicing optimizations of the base collection can kick in.
-  //
-  // We can't do that right now though, because that would force a lot of
-  // constraints on `Base.SubSequence`, limiting the possible contexts where
-  // the `.lazy.filter` API can be used.
+  public typealias SubSequence = ${Self}<Base.SubSequence>
 
   /// Returns an iterator over the elements of this sequence.
   ///
@@ -310,11 +248,12 @@ extension LazySequenceProtocol {
 % for Traversal in ['Forward', 'Bidirectional']:
 
 extension LazyCollectionProtocol
-%   if Traversal != 'Forward':
   where
+%   if Traversal != 'Forward':
   Self : ${collectionForTraversal(Traversal)},
-  Elements : ${collectionForTraversal(Traversal)}
+  Elements : ${collectionForTraversal(Traversal)},
 %   end
+  Self.Elements.SubSequence : ${collectionForTraversal(Traversal)}
 {
   /// Returns the elements of `self` that satisfy `predicate`.
   ///
diff --git a/test/stdlib/Filter.swift b/test/stdlib/Filter.swift
index 83721212c12ae..bb5bce762853b 100644
--- a/test/stdlib/Filter.swift
+++ b/test/stdlib/Filter.swift
@@ -32,12 +32,6 @@ extension LazyFilterSequence where Base : TestProtocol1 {
   }
 }
 
-extension LazyFilterIndex where Base : TestProtocol1 {
-  var _baseIsTestProtocol1: Bool {
-    fatalError("not implemented")
-  }
-}
-
 extension LazyFilterCollection where Base : TestProtocol1 {
   var _baseIsTestProtocol1: Bool {
     fatalError("not implemented")
diff --git a/test/stdlib/Renames.swift b/test/stdlib/Renames.swift
index 34f1c4d401a08..d1daaf4a91cdf 100644
--- a/test/stdlib/Renames.swift
+++ b/test/stdlib/Renames.swift
@@ -171,7 +171,7 @@ func _Filter<S : Sequence>(s: S) {
 func _Filter<S>(s: LazyFilterSequence<S>) {
   _ = s.generate() // expected-error {{'generate()' has been renamed to 'makeIterator()'}} {{9-17=makeIterator}} {{none}}
 }
-func _Filter<C : Collection>(c: C) {
+func _Filter<C : Collection>(c: C) where C.SubSequence: Collection {
   _ = LazyFilterCollection(c) { _ in true} // expected-error {{'init(_:whereElementsSatisfy:)' is unavailable: use '.lazy.filter' on the collection}}
 }
 func _Filter<C>(c: LazyFilterCollection<C>) {
diff --git a/validation-test/stdlib/Lazy.swift.gyb b/validation-test/stdlib/Lazy.swift.gyb
index db741c9ece8ec..f8ffca239a94e 100644
--- a/validation-test/stdlib/Lazy.swift.gyb
+++ b/validation-test/stdlib/Lazy.swift.gyb
@@ -638,10 +638,10 @@ tests.test("LazySequence/Sequence") {
 }
 
 func expectSequencePassthrough<
-  S : Sequence,
+  S : LazySequenceProtocol,
   Base : Sequence
 >(_ s: S, base: Base, arbitraryElement: S.Iterator.Element, count: Int)
-where S : LazySequenceProtocol, Base : LoggingType,
+where Base : LoggingType,
 Base.Iterator.Element == S.Iterator.Element {
   let baseType = type(of: base)
 
@@ -825,7 +825,7 @@ tests.test("LazyMapCollection/Passthrough") {
   let startIndex = CollectionLog.startIndex.expectIncrement(type(of: base)) {
     mapped.startIndex
   }
-  let endIndex = CollectionLog.endIndex.expectIncrement(type(of: base)) {
+  _ = CollectionLog.endIndex.expectIncrement(type(of: base)) {
     mapped.endIndex
   }
   // Not exactly passthrough, because mapping transforms the result
@@ -1023,9 +1023,7 @@ tests.test("ReversedCollection/Lazy") {
 // Given a couple of sequences backed by FilterGenerator's, check that
 // the first selects even numbers and the second selects odd numbers,
 // both from an underlying sequence of whole numbers.
-func checkFilterIteratorBase<
-  S : Sequence, I : IteratorProtocol
->(_ s1: S, _ s2: S)
+func checkFilterIteratorBase<  S : Sequence, I>(_ s1: S, _ s2: S)
 where S.Iterator == LazyFilterIterator<I>, I.Element == OpaqueValue<Int> {
   var iter1 = s1.makeIterator()
   expectEqual(0, iter1.next()!.value)
@@ -1098,16 +1096,16 @@ tests.test("LazyFilterIndex/base") {
   let evens = base.lazy.filter { $0.value % 2 == 0 }
   let odds = base.lazy.filter { $0.value % 2 != 0 }
 
-  expectEqual(base.startIndex, evens.startIndex.base)
-  expectEqual(base.index(after: base.startIndex), odds.startIndex.base)
+  expectEqual(base.startIndex, evens.startIndex)
+  expectEqual(base.index(after: base.startIndex), odds.startIndex)
 
   expectEqual(
     base.index(after: base.index(after: base.startIndex)),
-    evens.index(after: evens.startIndex).base)
+    evens.index(after: evens.startIndex))
 
   expectEqual(
     base.index(after: base.index(after: base.index(after: base.startIndex))),
-    odds.index(after: odds.startIndex).base)
+    odds.index(after: odds.startIndex))
 }
 
 tests.test("LazyFilterCollection") {
@@ -1157,8 +1155,7 @@ tests.test("LazyFilterCollection/AssociatedTypes") {
   expectCollectionAssociatedTypes(
     collectionType: Subject.self,
     iteratorType: LazyFilterIterator<Base.Iterator>.self,
-    // FIXME(ABI)#80 (Associated Types with where clauses): SubSequence should be `LazyFilterCollection<Base.Slice>`.
-    subSequenceType: Slice<Subject>.self,
+    subSequenceType: LazyFilterCollection<Base.SubSequence>.self,
     indexType: LazyFilterIndex<Base>.self,
     indexDistanceType: Base.IndexDistance.self,
     indicesType: DefaultIndices<Subject>.self)
@@ -1170,8 +1167,7 @@ tests.test("LazyFilterBidirectionalCollection/AssociatedTypes") {
   expectBidirectionalCollectionAssociatedTypes(
     collectionType: Subject.self,
     iteratorType: LazyFilterIterator<Base.Iterator>.self,
-    // FIXME(ABI)#81 (Associated Types with where clauses): SubSequence should be `LazyFilterBidirectionalCollection<Base.Slice>`.
-    subSequenceType: BidirectionalSlice<Subject>.self,
+    subSequenceType: LazyFilterBidirectionalCollection<Base.SubSequence>.self,
     indexType: LazyFilterIndex<Base>.self,
     indexDistanceType: Base.IndexDistance.self,
     indicesType: DefaultBidirectionalIndices<Subject>.self)