diff --git a/internal/lsp/source/completion.go b/internal/lsp/source/completion.go
index e060c2b1..805c441a 100644
--- a/internal/lsp/source/completion.go
+++ b/internal/lsp/source/completion.go
@@ -1028,14 +1028,28 @@ func (c *completer) matchingType(cand *candidate) bool {
 	// are invoked by default.
 	cand.expandFuncCall = isFunc(cand.obj)
 
-	typeMatches := func(actual types.Type) bool {
+	typeMatches := func(candType types.Type) bool {
 		// Take into account any type modifiers on the expected type.
-		actual = c.expectedType.applyTypeModifiers(actual)
+		candType = c.expectedType.applyTypeModifiers(candType)
 
 		if c.expectedType.objType != nil {
+			wantType := types.Default(c.expectedType.objType)
+
+			// Handle untyped values specially since AssignableTo gives false negatives
+			// for them (see https://golang.org/issue/32146).
+			if candBasic, ok := candType.(*types.Basic); ok && candBasic.Info()&types.IsUntyped > 0 {
+				if wantBasic, ok := wantType.Underlying().(*types.Basic); ok {
+					// Check that their constant kind (bool|int|float|complex|string) matches.
+					// This doesn't take into account the constant value, so there will be some
+					// false positives due to integer sign and overflow.
+					return candBasic.Info()&types.IsConstType == wantBasic.Info()&types.IsConstType
+				}
+				return false
+			}
+
 			// AssignableTo covers the case where the types are equal, but also handles
 			// cases like assigning a concrete type to an interface type.
-			return types.AssignableTo(types.Default(actual), types.Default(c.expectedType.objType))
+			return types.AssignableTo(candType, wantType)
 		}
 
 		return false
diff --git a/internal/lsp/testdata/rank/convert_rank.go.in b/internal/lsp/testdata/rank/convert_rank.go.in
index dc0a3a5e..fe6b7831 100644
--- a/internal/lsp/testdata/rank/convert_rank.go.in
+++ b/internal/lsp/testdata/rank/convert_rank.go.in
@@ -10,3 +10,30 @@ func _() {
 	)
 	wantsStrList(strList(conv)) //@complete("))", convertB, convertA)
 }
+
+func _() {
+	const (
+		convC        = "hi"    //@item(convertC, "convC", "string", "const")
+		convD        = 123     //@item(convertD, "convD", "int", "const")
+		convE int    = 123     //@item(convertE, "convE", "int", "const")
+		convF string = "there" //@item(convertF, "convF", "string", "const")
+	)
+
+	var foo int
+	foo = conv //@complete(" //", convertD, convertE, convertC, convertF)
+
+	type myInt int
+	var mi myInt
+	mi = conv //@complete(" //", convertD, convertC, convertE, convertF)
+	mi + conv //@complete(" //", convertD, convertC, convertE, convertF)
+
+	1 + conv //@complete(" //", convertD, convertE, convertC, convertF)
+
+	type myString string
+	var ms myString
+	ms = conv //@complete(" //", convertC, convertD, convertE, convertF)
+
+	type myUint uint32
+	var mu myUint
+	mu = conv //@complete(" //", convertD, convertC, convertE, convertF)
+}
diff --git a/internal/lsp/tests/tests.go b/internal/lsp/tests/tests.go
index 6b6c39f2..65a29f39 100644
--- a/internal/lsp/tests/tests.go
+++ b/internal/lsp/tests/tests.go
@@ -25,7 +25,7 @@ import (
 // We hardcode the expected number of test cases to ensure that all tests
 // are being executed. If a test is added, this number must be changed.
 const (
-	ExpectedCompletionsCount       = 138
+	ExpectedCompletionsCount       = 144
 	ExpectedCompletionSnippetCount = 15
 	ExpectedDiagnosticsCount       = 17
 	ExpectedFormatCount            = 5