diff --git a/compiler/src/dotty/tools/dotc/core/Types.scala b/compiler/src/dotty/tools/dotc/core/Types.scala
index 7cdcf767f8a2..52ce035ed327 100644
--- a/compiler/src/dotty/tools/dotc/core/Types.scala
+++ b/compiler/src/dotty/tools/dotc/core/Types.scala
@@ -3286,7 +3286,7 @@ object Types {
    *  `owningTree` and `owner` are used to determine whether a type-variable can be instantiated
    *  at some given point. See `Inferencing#interpolateUndetVars`.
    */
-  final class TypeVar(val origin: TypeParamRef, creatorState: TyperState, val bindingTree: untpd.Tree, val owner: Symbol) extends CachedProxyType with ValueType {
+  final class TypeVar(val origin: TypeParamRef, creatorState: TyperState, var bindingTree: untpd.Tree, val owner: Symbol) extends CachedProxyType with ValueType {
 
     /** The permanent instance type of the variable, or NoType is none is given yet */
     private[this] var myInst: Type = NoType
diff --git a/compiler/src/dotty/tools/dotc/typer/EtaExpansion.scala b/compiler/src/dotty/tools/dotc/typer/EtaExpansion.scala
index be84427a83a0..2f39b07aa998 100644
--- a/compiler/src/dotty/tools/dotc/typer/EtaExpansion.scala
+++ b/compiler/src/dotty/tools/dotc/typer/EtaExpansion.scala
@@ -167,26 +167,45 @@ object EtaExpansion extends LiftImpure {
    *
    *         { val xs = es; expr }
    *
-   *  If xarity matches the number of parameters in `mt`, the eta-expansion is
+   *  The result of the eta-expansion is either (1)
    *
    *         { val xs = es; (x1, ..., xn) => expr(x1, ..., xn) }
    *
-   * Note that the function value's parameters are untyped, hence the type will
-   * be supplied by the environment (or if missing be supplied by the target
-   * method as a fallback). On the other hand, if `xarity` is different from
-   * the number of parameters in `mt`, then we cannot propagate parameter types
-   * from the expected type, and we fallback to using the method's original
-   * parameter types instead.
+   *  or (2)
    *
-   * In either case, the result is an untyped tree, with `es` and `expr` as typed splices.
+   *         { val xs = es; (x1: T1, ..., xn: Tn) => expr(x1, ..., xn) }
+   *
+   *  or (3)
+   *
+   *         { val xs = es; (x1: T1, ..., xn: Tn) => expr(x1, ..., xn) _ }
+   *
+   *  where `T1, ..., Tn` are the paremeter types of the expanded method.
+   *
+   *  Case (3) applies if the method is curried, i.e. its result type is again a method
+   *  type. Case (2) applies if the expected arity of the function type `xarity` differs
+   *  from the number of parameters in `mt`. Case (1) applies if `mt` is uncurried
+   *  and its number of parameters equals `xarity`. In this case we can always infer
+   *  the parameter types later from the callee even if parameter types could not be
+   *  inferred from the expected type. Hence, we lose nothing by omitting parameter types
+   *  in the eta expansion. On the other hand omitting these parameters keeps the possibility
+   *  open that different parameters are inferred from the expected type, so we keep
+   *  more options open.
+   *
+   *  In each case, the result is an untyped tree, with `es` and `expr` as typed splices.
+   *
+   *    F[V](x) ==> (x => F[X])
    */
   def etaExpand(tree: Tree, mt: MethodType, xarity: Int)(implicit ctx: Context): untpd.Tree = {
     import untpd._
     assert(!ctx.isAfterTyper)
     val defs = new mutable.ListBuffer[tpd.Tree]
     val lifted: Tree = TypedSplice(liftApp(defs, tree))
+    val isLastApplication = mt.resultType match {
+      case rt: MethodType => rt.isImplicitMethod
+      case _ => true
+    }
     val paramTypes: List[Tree] =
-      if (mt.paramInfos.length == xarity) mt.paramInfos map (_ => TypeTree())
+      if (isLastApplication && mt.paramInfos.length == xarity) mt.paramInfos map (_ => TypeTree())
       else mt.paramInfos map TypeTree
     val params = (mt.paramNames, paramTypes).zipped.map((name, tpe) =>
       ValDef(name, tpe, EmptyTree).withFlags(Synthetic | Param).withPos(tree.pos.startPos))
@@ -194,10 +213,7 @@ object EtaExpansion extends LiftImpure {
     if (mt.paramInfos.nonEmpty && mt.paramInfos.last.isRepeatedParam)
       ids = ids.init :+ repeated(ids.last)
     var body: Tree = Apply(lifted, ids)
-    mt.resultType match {
-      case rt: MethodType if !rt.isImplicitMethod => body = PostfixOp(body, Ident(nme.WILDCARD))
-      case _ =>
-    }
+    if (!isLastApplication) body = PostfixOp(body, Ident(nme.WILDCARD))
     val fn = untpd.Function(params, body)
     if (defs.nonEmpty) untpd.Block(defs.toList map (untpd.TypedSplice(_)), fn) else fn
   }
diff --git a/compiler/src/dotty/tools/dotc/typer/Inferencing.scala b/compiler/src/dotty/tools/dotc/typer/Inferencing.scala
index 9b5d9d29c846..9219bcdd8979 100644
--- a/compiler/src/dotty/tools/dotc/typer/Inferencing.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Inferencing.scala
@@ -166,7 +166,7 @@ object Inferencing {
       case Apply(fn, _) => boundVars(fn, acc)
       case TypeApply(fn, targs) =>
         val tvars = targs.tpes.collect {
-          case tvar: TypeVar if !tvar.isInstantiated => tvar
+          case tvar: TypeVar if !tvar.isInstantiated && targs.contains(tvar.bindingTree) => tvar
         }
         boundVars(fn, acc ::: tvars)
       case Select(pre, _) => boundVars(pre, acc)
@@ -394,6 +394,20 @@ trait Inferencing { this: Typer =>
     }
     if (constraint.uninstVars exists qualifies) interpolate()
   }
+
+  /** The uninstantiated type variables introduced somehwere in `tree` */
+  def uninstBoundVars(tree: Tree)(implicit ctx: Context): List[TypeVar] = {
+    val buf = new mutable.ListBuffer[TypeVar]
+    tree.foreachSubTree {
+      case TypeApply(_, args) =>
+        args.tpes.foreach {
+          case tv: TypeVar if !tv.isInstantiated && tree.contains(tv.bindingTree) => buf += tv
+          case _ =>
+        }
+      case _ =>
+    }
+    buf.toList
+  }
 }
 
 /** An enumeration controlling the degree of forcing in "is-dully-defined" checks. */
diff --git a/compiler/src/dotty/tools/dotc/typer/Typer.scala b/compiler/src/dotty/tools/dotc/typer/Typer.scala
index fc56b72eef12..750bbcabb145 100644
--- a/compiler/src/dotty/tools/dotc/typer/Typer.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Typer.scala
@@ -1970,7 +1970,7 @@ class Typer extends Namer
       if (!tree.denot.isOverloaded) {
       	// for overloaded trees: resolve overloading before simplifying
         if (tree.isDef) interpolateUndetVars(tree, tree.symbol, pt)
-        else if (!tree.tpe.widen.isInstanceOf[LambdaType]) interpolateUndetVars(tree, NoSymbol, pt)
+        else if (!tree.tpe.widen.isInstanceOf[MethodOrPoly]) interpolateUndetVars(tree, NoSymbol, pt)
         tree.overwriteType(tree.tpe.simplified)
       }
       adaptInterpolated(tree, pt)
@@ -2227,8 +2227,18 @@ class Typer extends Namer
       if (arity >= 0 &&
           !tree.symbol.isConstructor &&
           !ctx.mode.is(Mode.Pattern) &&
-          !(isSyntheticApply(tree) && !isExpandableApply))
-        typed(etaExpand(tree, wtp, arity), pt)
+          !(isSyntheticApply(tree) && !isExpandableApply)) {
+        // Eta expansion interacts in tricky ways with type variable instantiation
+        // because it can extend the region where type variables are bound (and therefore may not
+        // be interpolated). To avoid premature interpolations, we need to extend the
+        // bindingTree of variables as we go along. Test case in pos/i3945.scala.
+        val boundtvs = uninstBoundVars(tree)
+        val uexpanded = etaExpand(tree, wtp, arity)
+        boundtvs.foreach(_.bindingTree = uexpanded) // make boundtvs point to uexpanded so that they are _not_ interpolated
+        val texpanded = typedUnadapted(uexpanded, pt)
+        boundtvs.foreach(_.bindingTree = texpanded) // make boundtvs point to texpanded so that they _can_ be interpolated
+        adapt(texpanded, pt)
+      }
       else if (wtp.paramInfos.isEmpty && isAutoApplied(tree.symbol))
         adaptInterpolated(tpd.Apply(tree, Nil), pt)
       else if (wtp.isImplicitMethod)
diff --git a/tests/pos/i3945.scala b/tests/pos/i3945.scala
new file mode 100644
index 000000000000..2533a67ca8d9
--- /dev/null
+++ b/tests/pos/i3945.scala
@@ -0,0 +1,19 @@
+object Test {
+  def int[A](k: String => A)(s: String)(x: Int): A = ???
+
+  // composing directly: ok in scalac, now also in dotc
+  val c: (String => String) => (String) => (Int) => (Int) => String = (int[Int => String](_)).compose(int[String](_))
+
+  // unwrapping composition: ok in scalac, ok in dotc
+  val q: (String => Int => String) => (String) => (Int) => (Int => String) = int[Int => String]
+  val p: (String => String) => (String) => (Int) => String = int
+  val c2: (String => String) => (String) => (Int) => (Int) => String = q.compose(p)
+
+  class B
+  class C extends B
+  implicit def iC: C => Unit = ???
+
+  // making sure A is not instantiated before implicit search
+  def f[A](k: String => A)(s: String)(x: Int)(implicit y: A => Unit): A = ???
+  val r: (String => C) => (String) => (Int) => B = f
+}