diff --git a/internal/core/adt/closed.go b/internal/core/adt/closed.go
index 9cf590b..25e431b 100644
--- a/internal/core/adt/closed.go
+++ b/internal/core/adt/closed.go
@@ -93,7 +93,8 @@
 type CloseInfo struct {
 	*closeInfo
 
-	IsClosed bool
+	IsClosed   bool
+	FieldTypes OptionalType
 }
 
 func (c CloseInfo) Location() Node {
diff --git a/internal/core/adt/composite.go b/internal/core/adt/composite.go
index 6f19b19..f128606 100644
--- a/internal/core/adt/composite.go
+++ b/internal/core/adt/composite.go
@@ -488,7 +488,7 @@
 
 // OptionalType is a bit field of the type of optional constraints in use by an
 // Acceptor.
-type OptionalType int
+type OptionalType int8
 
 const (
 	HasField          OptionalType = 1 << iota // X: T
diff --git a/internal/core/adt/eval.go b/internal/core/adt/eval.go
index addd784..2ebc66f 100644
--- a/internal/core/adt/eval.go
+++ b/internal/core/adt/eval.go
@@ -385,9 +385,16 @@
 // insertConjuncts inserts conjuncts previously uninserted.
 func (n *nodeContext) insertConjuncts() {
 	for len(n.conjuncts) > 0 {
-		x := n.conjuncts[0]
+		nInfos := len(n.node.Structs)
+		p := &n.conjuncts[0]
 		n.conjuncts = n.conjuncts[1:]
-		n.addExprConjunct(x)
+		n.addExprConjunct(*p)
+
+		// Record the OptionalTypes for all structs that were inferred by this
+		// Conjunct. This information can be used by algorithms such as trim.
+		for i := nInfos; i < len(n.node.Structs); i++ {
+			p.CloseInfo.FieldTypes |= n.node.Structs[i].types
+		}
 	}
 }
 
diff --git a/tools/trim/testdata/constraintroots.txtar b/tools/trim/testdata/constraintroots.txtar
new file mode 100644
index 0000000..7f47d4b
--- /dev/null
+++ b/tools/trim/testdata/constraintroots.txtar
@@ -0,0 +1,104 @@
+// Issue #716
+-- in.cue --
+keepPatternConstraintRoot: {
+	if true {
+		deployment: "name": {spec: []}
+	}
+
+	deployment: name: spec: []
+
+	deployment: [string]: spec: []
+}
+
+// TODO(additional): add once implemented
+// keepAdditionalRoots: {
+// 	if true {
+//		deployment: "name": {spec: [1]}
+//	}
+//
+//	deployment: name: spec: [1]
+//
+//	deployment: [string]: spec: [1]
+// }
+
+keepPatternConstraintRootSolo: {
+	if true {
+		deployment: "name": {spec: [1]}
+	}
+
+	deployment: [string]: spec: [1]
+}
+
+keepPatternConstraintRootIndirect: {
+	if true {
+		deployment: "name": {spec: []}
+	}
+
+	deployment: name: spec: []
+
+	deployment: indirect
+
+	indirect: {{[string]: spec: []}}
+}
+
+keepPatternConstraintRootDef: {
+	if true {
+		deployment: "name": {spec: []}
+	}
+
+	#Deployment: spec: []
+
+	deployment: name: #Deployment
+
+	deployment: [string]: spec: []
+}
+
+
+-- out/trim --
+== in.cue
+keepPatternConstraintRoot: {
+	if true {
+		deployment: "name": {spec: []}
+	}
+
+	deployment: [string]: spec: []
+}
+
+// TODO(additional): add once implemented
+// keepAdditionalRoots: {
+//  if true {
+//   deployment: "name": {spec: [1]}
+//  }
+//
+// deployment: name: spec: [1]
+//
+// deployment: [string]: spec: [1]
+// }
+
+keepPatternConstraintRootSolo: {
+	if true {
+		deployment: "name": {spec: [1]}
+	}
+
+	deployment: [string]: spec: [1]
+}
+
+keepPatternConstraintRootIndirect: {
+	if true {
+		deployment: "name": {spec: []}
+	}
+
+	deployment: indirect
+
+	indirect: {{[string]: spec: []}}
+}
+
+keepPatternConstraintRootDef: {
+	if true {
+		deployment: "name": {spec: []}
+	}
+
+	#Deployment: spec: []
+
+	deployment: [string]: spec: []
+}
diff --git a/tools/trim/testdata/rmimport.txtar b/tools/trim/testdata/rmimport.txtar
new file mode 100644
index 0000000..f48431f
--- /dev/null
+++ b/tools/trim/testdata/rmimport.txtar
@@ -0,0 +1,38 @@
+// Issue #716
+//
+// NOTE removing the empty import decl is more a job for
+// cue/format or astutil.Sanitize.
+
+-- a/a.cue --
+package a
+
+A: 5
+-- b.cue --
+package b
+
+import (
+	"example.com/blah/a"
+)
+
+#Def: {
+    y: 5
+}
+
+x: #Def
+x: y: a.A
+-- cue.mod/module.cue --
+module: "example.com/blah"
+
+-- out/trim --
+== b.cue
+package b
+
+import (
+)
+
+#Def: {
+	y: 5
+}
+
+x: #Def
+x: {}
diff --git a/tools/trim/trim.go b/tools/trim/trim.go
index 17e164c..96a6a03 100644
--- a/tools/trim/trim.go
+++ b/tools/trim/trim.go
@@ -89,6 +89,9 @@
 			}
 			return true
 		}, nil)
+		if err := astutil.Sanitize(f); err != nil {
+			return err
+		}
 	}
 
 	return nil
@@ -109,10 +112,18 @@
 
 const dominatorNode = adt.ComprehensionSpan | adt.DefinitionSpan | adt.ConstraintSpan
 
+// isDominator reports whether a node can remove other nodes.
 func isDominator(c adt.Conjunct) bool {
 	return c.CloseInfo.IsInOneOf(dominatorNode)
 }
 
+// Removable reports whether a non-dominator conjunct can be removed. This is
+// not the case if it has pattern constraints that could turn into dominator
+// nodes.
+func removable(c adt.Conjunct) bool {
+	return c.CloseInfo.FieldTypes&(adt.HasAdditional|adt.HasPattern) == 0
+}
+
 // Roots of constraints are not allowed to strip conjuncts by
 // themselves as it will eliminate the reason for the trigger.
 func allowRemove(v *adt.Vertex) bool {
@@ -200,7 +211,7 @@
 	}
 
 	for _, c := range v.Conjuncts {
-		if !isDominator(c) {
+		if !isDominator(c) && removable(c) {
 			t.markRemove(c)
 		}
 	}