diff --git a/packages/ERTP/src/amountMath.js b/packages/ERTP/src/amountMath.js
index 2820cdc9c95..ab7d49ab681 100644
--- a/packages/ERTP/src/amountMath.js
+++ b/packages/ERTP/src/amountMath.js
@@ -200,9 +200,10 @@ const AmountMath = {
    * Make an amount from a value by adding the brand.
    *
    * @template {AssetKind} K
+   * @template {Key} [M=any] member kind
    * @param {Brand<K>} brand
-   * @param {AssetValueForKind<K>} allegedValue
-   * @returns {Amount<K>}
+   * @param {AssetValueForKind<K, M>} allegedValue
+   * @returns {Amount<K, M>}
    */
   // allegedValue has a conditional expression for type widening, to prevent V being bound to a a literal like 1n
   make: (brand, allegedValue) => {
diff --git a/packages/ERTP/src/types-ambient.js b/packages/ERTP/src/types-ambient.js
index 073d6cc17c6..b9797dfeb6a 100644
--- a/packages/ERTP/src/types-ambient.js
+++ b/packages/ERTP/src/types-ambient.js
@@ -9,6 +9,7 @@
 
 /**
  * @template {AssetKind} [K=AssetKind]
+ * @template {Key} [M=Key] member kind, for Amounts that have member values
  * @typedef {object} Amount Amounts are descriptions of digital assets,
  *   answering the questions "how much" and "of what kind". Amounts are values
  *   labeled with a brand. AmountMath executes the logic of how amounts are
@@ -18,7 +19,7 @@
  *   bucks. AmountMath relies heavily on polymorphic MathHelpers, which
  *   manipulate the unbranded portion.
  * @property {Brand<K>} brand
- * @property {AssetValueForKind<K>} value
+ * @property {AssetValueForKind<K, M>} value
  */
 
 /**
@@ -51,14 +52,15 @@
 
 /**
  * @template {AssetKind} K
+ * @template {Key} [M=Key] member kind, for Amounts that have member values
  * @typedef {K extends 'nat'
  *   ? NatValue
  *   : K extends 'set'
- *   ? SetValue
+ *   ? SetValue<M>
  *   : K extends 'copySet'
- *   ? CopySet
+ *   ? CopySet<M>
  *   : K extends 'copyBag'
- *   ? CopyBag
+ *   ? CopyBag<M>
  *   : never} AssetValueForKind
  */
 
@@ -93,10 +95,10 @@
 
 /**
  * @template {AssetKind} [K=AssetKind]
- * @typedef {object} Brand The brand identifies the kind of issuer, and has a
- *   function to get the alleged name for the kind of asset described. The
- *   alleged name (such as 'BTC' or 'moola') is provided by the maker of the
- *   issuer and should not be trusted as accurate.
+ * @typedef {import('@endo/marshal').RemotableObject} Brand The brand identifies
+ *   the kind of issuer, and has a function to get the alleged name for the kind
+ *   of asset described. The alleged name (such as 'BTC' or 'moola') is provided
+ *   by the maker of the issuer and should not be trusted as accurate.
  *
  *   Every amount created by a particular AmountMath will share the same brand,
  *   but recipients cannot rely on the brand to verify that a purported amount
@@ -289,12 +291,12 @@
 
 /**
  * @template {AssetKind} [K=AssetKind]
- * @typedef {object} Payment Payments hold amount of digital assets of the same
- *   brand in transit. Payments can be deposited in purses, split into multiple
- *   payments, combined, and claimed (getting an exclusive payment). Payments
- *   are linear, meaning that either a payment has the same amount of digital
- *   assets it started with, or it is used up entirely. It is impossible to
- *   partially use a payment.
+ * @typedef {import('@endo/marshal').RemotableObject} Payment Payments hold
+ *   amount of digital assets of the same brand in transit. Payments can be
+ *   deposited in purses, split into multiple payments, combined, and claimed
+ *   (getting an exclusive payment). Payments are linear, meaning that either a
+ *   payment has the same amount of digital assets it started with, or it is
+ *   used up entirely. It is impossible to partially use a payment.
  *
  *   Payments are often received from other actors and therefore should not be
  *   trusted themselves. To get the amount of digital assets in a payment, use
diff --git a/packages/zoe/tools/fakePriceAuthority.js b/packages/zoe/tools/fakePriceAuthority.js
index 625f3cf5b2a..a62405ba3f4 100644
--- a/packages/zoe/tools/fakePriceAuthority.js
+++ b/packages/zoe/tools/fakePriceAuthority.js
@@ -115,16 +115,19 @@ export async function makeFakePriceAuthority(options) {
       natSafeMath.multiply(amountIn.value, tradeValueOut),
       tradeValueIn,
     );
+    /** @type {Amount<'set', PriceDescription>} */
     const quoteAmount = AmountMath.make(
       quoteBrand,
-      harden([
-        {
-          amountIn,
-          amountOut: AmountMath.make(actualBrandOut, valueOut),
-          timer,
-          timestamp: quoteTime,
-        },
-      ]),
+      /** @type {[PriceDescription]} */ (
+        harden([
+          {
+            amountIn,
+            amountOut: AmountMath.make(actualBrandOut, valueOut),
+            timer,
+            timestamp: quoteTime,
+          },
+        ])
+      ),
     );
     const quote = harden({
       quotePayment: E(quoteMint).mintPayment(quoteAmount),
diff --git a/packages/zoe/tools/types-ambient.js b/packages/zoe/tools/types-ambient.js
index f34db44c459..ed50b345a1f 100644
--- a/packages/zoe/tools/types-ambient.js
+++ b/packages/zoe/tools/types-ambient.js
@@ -2,7 +2,7 @@
 
 /**
  * @typedef {object} PriceQuote
- * @property {Amount<'set'>} quoteAmount
+ * @property {Amount<'set', PriceDescription>} quoteAmount
  * Amount whose value is a PriceQuoteValue
  * @property {ERef<Payment<'set'>>} quotePayment
  * The `quoteAmount` wrapped as a payment