diff --git a/internal/pkg/types.go b/internal/pkg/types.go
index e7e3bfb62..801971bcc 100644
--- a/internal/pkg/types.go
+++ b/internal/pkg/types.go
@@ -62,7 +62,7 @@ func (s *Struct) Len() int {
 	return count
 }
 
-// IsOpen reports whether s allows more fields than are currently defined.
+// IsOpen reports whether s is open or has pattern constraints.
 func (s *Struct) IsOpen() bool {
 	if !s.node.IsClosedStruct() {
 		return true
@@ -77,6 +77,18 @@ func (s *Struct) IsOpen() bool {
 	return ot&^adt.HasDynamic != 0
 }
 
+// NumConstraintFields reports the number of explicit optional and required
+// fields, excluding pattern constraints.
+func (s Struct) NumConstraintFields() (count int) {
+	// If we have any optional arcs, we allow more fields.
+	for _, a := range s.node.Arcs {
+		if a.ArcType != adt.ArcMember && a.Label.IsRegular() {
+			count++
+		}
+	}
+	return count
+}
+
 // A ValidationError indicates an error that is only valid if a builtin is used
 // as a validator.
 type ValidationError struct {
diff --git a/pkg/struct/struct.go b/pkg/struct/struct.go
index 39e2cda40..a56848886 100644
--- a/pkg/struct/struct.go
+++ b/pkg/struct/struct.go
@@ -30,7 +30,7 @@ import (
 func MinFields(object pkg.Struct, n int) (bool, error) {
 	count := object.Len()
 	code := adt.EvalError
-	if object.IsOpen() {
+	if object.IsOpen() || count+object.NumConstraintFields() >= n {
 		code = adt.IncompleteError
 	}
 	if count < n {
diff --git a/pkg/struct/testdata/struct.txtar b/pkg/struct/testdata/struct.txtar
index 9c89f9614..bf8975307 100644
--- a/pkg/struct/testdata/struct.txtar
+++ b/pkg/struct/testdata/struct.txtar
@@ -1,13 +1,16 @@
 -- in.cue --
 import "struct"
 
-minFields: {
+minFields1: {
 	[string]: struct.MinFields(1)
 
 	incomplete1: {}
+	optIncomplete: {a?: string}
+
 	fail1: close({})
-	failOptional1: close({a?: 1})
+	optCloseIncomplete: close({a?: 1})
 	failHidden1: close({_a: 1})
+
 	ok4: {_a: 1, a: 1}
 	ok1: {a: 1}
 	ok2: close({a: 1})
@@ -15,6 +18,17 @@ minFields: {
 	ok5: {#a: int, a: #a & 1}
 }
 
+minFields2: {
+	[string]: struct.MinFields(2)
+
+	incomplete1: close({a?: string, b: 1})
+	incomplete2: close({a?: string, b?: int})
+	incomplete3: close({a?: string, b?: int, c: 1})
+	incomplete4: close({a?: string, b?: int, c?: int})
+
+	fail: close({a?: string})
+}
+
 maxFields: {
 	[string]: struct.MaxFields(1)
 
@@ -30,27 +44,32 @@ maxFields: {
 
 -- out/structs-v3 --
 Errors:
-minFields.fail1: invalid value {} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1):
-    ./in.cue:4:12
-    ./in.cue:4:29
-minFields.failHidden1: invalid value {_a:1} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1):
+minFields1.fail1: invalid value {} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1):
     ./in.cue:4:12
     ./in.cue:4:29
-minFields.failOptional1: invalid value {a?:1} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1):
+minFields1.failHidden1: invalid value {_a:1} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1):
     ./in.cue:4:12
     ./in.cue:4:29
+minFields2.fail: invalid value {a?:string} (does not satisfy struct.MinFields(2)): len(fields) < MinFields(2) (0 < 2):
+    ./in.cue:21:12
+    ./in.cue:21:29
 maxFields.fail1: invalid value {a:1,b:2} (does not satisfy struct.MaxFields(1)): len(fields) > MaxFields(1) (2 > 1):
-    ./in.cue:18:12
-    ./in.cue:18:29
+    ./in.cue:32:12
+    ./in.cue:32:29
 
 Result:
 import "struct"
 
-minFields: {
+minFields1: {
 	incomplete1: {} & struct.MinFields(1)
-	fail1:         _|_ // minFields.fail1: invalid value {} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1)
-	failOptional1: _|_ // minFields.failOptional1: invalid value {a?:1} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1)
-	failHidden1:   _|_ // minFields.failHidden1: invalid value {_a:1} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1)
+	optIncomplete: {
+		a?: string
+	} & struct.MinFields(1)
+	fail1: _|_ // minFields1.fail1: invalid value {} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1)
+	optCloseIncomplete: close({
+		a?: 1
+	}) & struct.MinFields(1)
+	failHidden1: _|_ // minFields1.failHidden1: invalid value {_a:1} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1)
 	ok4: {
 		a: 1
 	}
@@ -68,6 +87,27 @@ minFields: {
 		a:  1
 	}
 }
+minFields2: {
+	incomplete1: close({
+		a?: string
+		b:  1
+	}) & struct.MinFields(2)
+	incomplete2: close({
+		a?: string
+		b?: int
+	}) & struct.MinFields(2)
+	incomplete3: close({
+		a?: string
+		b?: int
+		c:  1
+	}) & struct.MinFields(2)
+	incomplete4: close({
+		a?: string
+		b?: int
+		c?: int
+	}) & struct.MinFields(2)
+	fail: _|_ // minFields2.fail: invalid value {a?:string} (does not satisfy struct.MinFields(2)): len(fields) < MinFields(2) (0 < 2)
+}
 maxFields: {
 	ok1: {}
 	ok2: {
@@ -89,74 +129,73 @@ maxFields: {
 	}
 	fail1: _|_ // maxFields.fail1: invalid value {a:1,b:2} (does not satisfy struct.MaxFields(1)): len(fields) > MaxFields(1) (2 > 1)
 }
--- diff/explanation --
-failOptional1: the new evaluator fails as expected, but the old evaluator doesn't -
-perhaps due to a bug in either the old evaluator or test code.
 -- diff/-out/structs-v3<==>+out/structs --
 diff old new
 --- old
 +++ new
 @@ -2,15 +2,15 @@
- minFields.fail1: invalid value {} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1):
+ minFields1.fail1: invalid value {} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1):
      ./in.cue:4:12
      ./in.cue:4:29
--    ./in.cue:7:9
- minFields.failHidden1: invalid value {_a:1} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1):
+-    ./in.cue:9:9
+ minFields1.failHidden1: invalid value {_a:1} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1):
      ./in.cue:4:12
      ./in.cue:4:29
--    ./in.cue:9:15
-+minFields.failOptional1: invalid value {a?:1} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1):
-+    ./in.cue:4:12
-+    ./in.cue:4:29
+-    ./in.cue:11:15
++minFields2.fail: invalid value {a?:string} (does not satisfy struct.MinFields(2)): len(fields) < MinFields(2) (0 < 2):
++    ./in.cue:21:12
++    ./in.cue:21:29
  maxFields.fail1: invalid value {a:1,b:2} (does not satisfy struct.MaxFields(1)): len(fields) > MaxFields(1) (2 > 1):
-     ./in.cue:18:12
-     ./in.cue:18:29
--    ./in.cue:27:9
+     ./in.cue:32:12
+     ./in.cue:32:29
+-    ./in.cue:41:9
  
  Result:
  import "struct"
-@@ -17,11 +17,9 @@
- 
- minFields: {
- 	incomplete1: {} & struct.MinFields(1)
--	fail1: _|_ // minFields.fail1: invalid value {} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1)
--	failOptional1: close({
--		a?: 1
--	}) & struct.MinFields(1)
--	failHidden1: _|_ // minFields.failHidden1: invalid value {_a:1} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1)
-+	fail1:         _|_ // minFields.fail1: invalid value {} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1)
-+	failOptional1: _|_ // minFields.failOptional1: invalid value {a?:1} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1)
-+	failHidden1:   _|_ // minFields.failHidden1: invalid value {_a:1} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1)
- 	ok4: {
- 		a: 1
- 	}
+@@ -61,9 +61,7 @@
+ 		b?: int
+ 		c?: int
+ 	}) & struct.MinFields(2)
+-	fail: close({
+-		a?: string
+-	}) & struct.MinFields(2)
++	fail: _|_ // minFields2.fail: invalid value {a?:string} (does not satisfy struct.MinFields(2)): len(fields) < MinFields(2) (0 < 2)
+ }
+ maxFields: {
+ 	ok1: {}
 -- diff/todo/p2 --
 Missing error positions.
+-- diff/explanation --
+minFields1.fail1: the new evaluator fails as expected. It is more precise than
+the old evaluator.
 -- out/structs --
 Errors:
-minFields.fail1: invalid value {} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1):
+minFields1.fail1: invalid value {} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1):
     ./in.cue:4:12
     ./in.cue:4:29
-    ./in.cue:7:9
-minFields.failHidden1: invalid value {_a:1} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1):
+    ./in.cue:9:9
+minFields1.failHidden1: invalid value {_a:1} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1):
     ./in.cue:4:12
     ./in.cue:4:29
-    ./in.cue:9:15
+    ./in.cue:11:15
 maxFields.fail1: invalid value {a:1,b:2} (does not satisfy struct.MaxFields(1)): len(fields) > MaxFields(1) (2 > 1):
-    ./in.cue:18:12
-    ./in.cue:18:29
-    ./in.cue:27:9
+    ./in.cue:32:12
+    ./in.cue:32:29
+    ./in.cue:41:9
 
 Result:
 import "struct"
 
-minFields: {
+minFields1: {
 	incomplete1: {} & struct.MinFields(1)
-	fail1: _|_ // minFields.fail1: invalid value {} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1)
-	failOptional1: close({
+	optIncomplete: {
+		a?: string
+	} & struct.MinFields(1)
+	fail1: _|_ // minFields1.fail1: invalid value {} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1)
+	optCloseIncomplete: close({
 		a?: 1
 	}) & struct.MinFields(1)
-	failHidden1: _|_ // minFields.failHidden1: invalid value {_a:1} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1)
+	failHidden1: _|_ // minFields1.failHidden1: invalid value {_a:1} (does not satisfy struct.MinFields(1)): len(fields) < MinFields(1) (0 < 1)
 	ok4: {
 		a: 1
 	}
@@ -174,6 +213,29 @@ minFields: {
 		a:  1
 	}
 }
+minFields2: {
+	incomplete1: close({
+		a?: string
+		b:  1
+	}) & struct.MinFields(2)
+	incomplete2: close({
+		a?: string
+		b?: int
+	}) & struct.MinFields(2)
+	incomplete3: close({
+		a?: string
+		b?: int
+		c:  1
+	}) & struct.MinFields(2)
+	incomplete4: close({
+		a?: string
+		b?: int
+		c?: int
+	}) & struct.MinFields(2)
+	fail: close({
+		a?: string
+	}) & struct.MinFields(2)
+}
 maxFields: {
 	ok1: {}
 	ok2: {