diff --git a/tiledb/api/src/array/schema.rs b/tiledb/api/src/array/schema.rs
index 6aa8d47c..442214e1 100644
--- a/tiledb/api/src/array/schema.rs
+++ b/tiledb/api/src/array/schema.rs
@@ -9,7 +9,7 @@ use crate::array::{Attribute, Domain, Layout};
 use crate::context::Context;
 use crate::Result as TileDBResult;
 
-#[derive(Clone, Debug, PartialEq)]
+#[derive(Clone, Copy, Debug, PartialEq)]
 pub enum ArrayType {
     Dense,
     Sparse,
diff --git a/tiledb/test/src/attribute.rs b/tiledb/test/src/attribute.rs
index d46e6ef8..90d7b7b2 100644
--- a/tiledb/test/src/attribute.rs
+++ b/tiledb/test/src/attribute.rs
@@ -5,6 +5,10 @@ use tiledb::context::Context;
 pub fn arbitrary_name() -> impl Strategy<Value = String> {
     proptest::string::string_regex("[a-zA-Z0-9_]*")
         .expect("Error creating attribute name strategy")
+        .prop_filter(
+            "Attribute names may not begin with reserved prefix",
+            |name| !name.starts_with("__"),
+        )
 }
 
 pub fn arbitrary(context: &Context) -> impl Strategy<Value = Attribute> {
diff --git a/tiledb/test/src/domain.rs b/tiledb/test/src/domain.rs
index 0e1a2a28..ddd92ed4 100644
--- a/tiledb/test/src/domain.rs
+++ b/tiledb/test/src/domain.rs
@@ -1,25 +1,32 @@
 use proptest::prelude::*;
-use tiledb::array::{Domain, DomainBuilder};
+use tiledb::array::{ArrayType, Domain, DomainBuilder};
 use tiledb::context::Context;
 use tiledb::Result as TileDBResult;
 
+use crate::strategy::LifetimeBoundStrategy;
+
 pub fn arbitrary(
     context: &Context,
+    array_type: ArrayType,
 ) -> impl Strategy<Value = TileDBResult<Domain>> {
     const MIN_DIMENSIONS: usize = 1;
     const MAX_DIMENSIONS: usize = 8;
 
-    proptest::collection::vec(
-        crate::dimension::arbitrary(context),
-        MIN_DIMENSIONS..=MAX_DIMENSIONS,
-    )
-    .prop_map(|dimensions| {
-        let mut d = DomainBuilder::new(context)?;
-        for dim in dimensions {
-            d = d.add_dimension(dim?)?;
-        }
-        Ok(d.build())
-    })
+    match array_type {
+        ArrayType::Dense => unimplemented!(),
+        ArrayType::Sparse => proptest::collection::vec(
+            crate::dimension::arbitrary(context),
+            MIN_DIMENSIONS..=MAX_DIMENSIONS,
+        )
+        .prop_map(|dimensions| {
+            let mut d = DomainBuilder::new(context)?;
+            for dim in dimensions {
+                d = d.add_dimension(dim?)?;
+            }
+            Ok(d.build())
+        })
+        .bind(),
+    }
 }
 
 #[cfg(test)]
@@ -28,11 +35,11 @@ mod tests {
 
     /// Test that the arbitrary domain construction always succeeds
     #[test]
-    fn domain_arbitrary() {
+    fn domain_arbitrary_sparse() {
         let ctx = Context::new().expect("Error creating context");
 
-        proptest!(|(maybe_domain in arbitrary(&ctx))| {
-            maybe_domain.expect("Error constructing arbitrary dimension");
+        proptest!(|(maybe_domain in arbitrary(&ctx, ArrayType::Sparse))| {
+            maybe_domain.expect("Error constructing arbitrary domain");
         });
     }
 }
diff --git a/tiledb/test/src/lib.rs b/tiledb/test/src/lib.rs
index 4857ebb2..5d9d9ef5 100644
--- a/tiledb/test/src/lib.rs
+++ b/tiledb/test/src/lib.rs
@@ -6,4 +6,5 @@ pub mod attribute;
 pub mod datatype;
 pub mod dimension;
 pub mod domain;
+pub mod schema;
 pub mod strategy;
diff --git a/tiledb/test/src/schema.rs b/tiledb/test/src/schema.rs
new file mode 100644
index 00000000..b7d1f38e
--- /dev/null
+++ b/tiledb/test/src/schema.rs
@@ -0,0 +1,49 @@
+use proptest::prelude::*;
+use tiledb::array::{ArrayType, Schema, SchemaBuilder};
+use tiledb::context::Context;
+use tiledb::Result as TileDBResult;
+
+pub fn arbitrary_array_type() -> impl Strategy<Value = ArrayType> {
+    // TODO: implement Domain scenario for Dense arrays
+    Just(ArrayType::Sparse)
+}
+
+pub fn arbitrary(
+    context: &Context,
+) -> impl Strategy<Value = TileDBResult<Schema>> {
+    const MIN_ATTRS: usize = 1;
+    const MAX_ATTRS: usize = 128;
+
+    arbitrary_array_type()
+        .prop_flat_map(move |array_type|
+            (
+                Just(array_type),
+                crate::domain::arbitrary(context, array_type),
+                proptest::collection::vec(crate::attribute::arbitrary(context), MIN_ATTRS..=MAX_ATTRS)
+            ))
+        .prop_map(|(array_type, domain, attrs)| {
+            /* TODO: cell order, tile order, capacity, duplicates */
+            let mut b = SchemaBuilder::new(context, array_type, domain?)?;
+            for attr in attrs {
+                /* TODO: how to ensure no duplicate names, assuming that matters? */
+                b = b.add_attribute(attr)?
+            }
+
+            Ok(b.build())
+        })
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    /// Test that the arbitrary schema construction always succeeds
+    #[test]
+    fn schema_arbitrary() {
+        let ctx = Context::new().expect("Error creating context");
+
+        proptest!(|(maybe_schema in arbitrary(&ctx))| {
+            maybe_schema.expect("Error constructing arbitrary schema");
+        });
+    }
+}