diff --git a/zebra-consensus/src/lib.rs b/zebra-consensus/src/lib.rs
index 8c105941b..aa1486c67 100644
--- a/zebra-consensus/src/lib.rs
+++ b/zebra-consensus/src/lib.rs
@@ -17,6 +17,7 @@
 pub mod block;
 pub mod checkpoint;
 pub mod mempool;
+pub mod parameters;
 pub mod redjubjub;
 mod script;
 mod transaction;
diff --git a/zebra-consensus/src/parameters.rs b/zebra-consensus/src/parameters.rs
new file mode 100644
index 000000000..488cfdcb7
--- /dev/null
+++ b/zebra-consensus/src/parameters.rs
@@ -0,0 +1,36 @@
+//! The consensus parameters for each Zcash network.
+//!
+//! Some consensus parameters change based on network upgrades. Each network
+//! upgrade happens at a particular block height. Some parameters have a value
+//! (or function) before the upgrade height, at the upgrade height, and after
+//! the upgrade height. (For example, the value of the reserved field in the
+//! block header during the Heartwood upgrade.)
+//!
+//! Typically, consensus parameters are accessed via a function that takes a
+//! `Network` and `BlockHeight`.
+
+use zebra_chain::block::BlockHeaderHash;
+use zebra_chain::{Network, Network::*};
+
+/// Returns the previous block hash for the genesis block in `network`.
+pub fn genesis_previous_block_hash(network: Network) -> BlockHeaderHash {
+    // All current networks use all-zeroes for the parent of the genesis block.
+    // (In Bitcoin, `null` is `[0; 32]`.)
+    //
+    // TODO: make this function const when feature(const_if_match) stabilises.
+    match network {
+        Mainnet | Testnet => BlockHeaderHash([0; 32]),
+    }
+}
+
+/// Returns the hash for the genesis block in `network`.
+pub fn genesis_hash(network: Network) -> BlockHeaderHash {
+    match network {
+        // zcash-cli getblockhash 0 | zebrad revhex
+        Mainnet => "08ce3d9731b000c08338455c8a4a6bd05da16e26b11daa1b917184ece80f0400",
+        // zcash-cli -testnet getblockhash 0 | zebrad revhex
+        Testnet => "382c4a332661c7ed0671f32a34d724619f086c61873bce7c99859dd9920aa605",
+    }
+    .parse()
+    .expect("hard-coded hash parses")
+}