diff --git a/src/Makefile.test.include b/src/Makefile.test.include
index c76f30de8..e7d7d76d3 100644
--- a/src/Makefile.test.include
+++ b/src/Makefile.test.include
@@ -209,7 +209,8 @@ BITCOIN_TESTS += \
   wallet/test/wallet_crypto_tests.cpp \
   wallet/test/coinselector_tests.cpp \
   wallet/test/init_tests.cpp \
-  wallet/test/ismine_tests.cpp
+  wallet/test/ismine_tests.cpp \
+  wallet/test/scriptpubkeyman_tests.cpp
 
 BITCOIN_TEST_SUITE += \
   wallet/test/wallet_test_fixture.cpp \
diff --git a/src/outputtype.cpp b/src/outputtype.cpp
index 567eecb5c..71b5cba01 100644
--- a/src/outputtype.cpp
+++ b/src/outputtype.cpp
@@ -82,30 +82,22 @@ CTxDestination AddAndGetDestinationForScript(FillableSigningProvider& keystore,
 {
     // Add script to keystore
     keystore.AddCScript(script);
-    ScriptHash sh(script);
     // Note that scripts over 520 bytes are not yet supported.
     switch (type) {
     case OutputType::LEGACY:
-        keystore.AddCScript(GetScriptForDestination(sh));
-        return sh;
+        return ScriptHash(script);
     case OutputType::P2SH_SEGWIT:
     case OutputType::BECH32: {
         CTxDestination witdest = WitnessV0ScriptHash(script);
         CScript witprog = GetScriptForDestination(witdest);
         // Check if the resulting program is solvable (i.e. doesn't use an uncompressed key)
-        if (!IsSolvable(keystore, witprog)) {
-            // Since the wsh is invalid, add and return the sh instead.
-            keystore.AddCScript(GetScriptForDestination(sh));
-            return sh;
-        }
+        if (!IsSolvable(keystore, witprog)) return ScriptHash(script);
         // Add the redeemscript, so that P2WSH and P2SH-P2WSH outputs are recognized as ours.
         keystore.AddCScript(witprog);
         if (type == OutputType::BECH32) {
             return witdest;
         } else {
-            ScriptHash sh_w = ScriptHash(witprog);
-            keystore.AddCScript(GetScriptForDestination(sh_w));
-            return sh_w;
+            return ScriptHash(witprog);
         }
     }
     default: assert(false);
diff --git a/src/script/signingprovider.h b/src/script/signingprovider.h
index 6ad20480a..76f31d2f6 100644
--- a/src/script/signingprovider.h
+++ b/src/script/signingprovider.h
@@ -66,7 +66,53 @@ protected:
     using KeyMap = std::map<CKeyID, CKey>;
     using ScriptMap = std::map<CScriptID, CScript>;
 
+    /**
+     * Map of key id to unencrypted private keys known by the signing provider.
+     * Map may be empty if the provider has another source of keys, like an
+     * encrypted store.
+     */
     KeyMap mapKeys GUARDED_BY(cs_KeyStore);
+
+    /**
+     * Map of script id to scripts known by the signing provider.
+     *
+     * This map originally just held P2SH redeemScripts, and was used by wallet
+     * code to look up script ids referenced in "OP_HASH160 <script id>
+     * OP_EQUAL" P2SH outputs. Later in 605e8473a7d it was extended to hold
+     * P2WSH witnessScripts as well, and used to look up nested scripts
+     * referenced in "OP_0 <script hash>" P2WSH outputs. Later in commits
+     * f4691ab3a9d and 248f3a76a82, it was extended once again to hold segwit
+     * "OP_0 <key or script hash>" scriptPubKeys, in order to give the wallet a
+     * way to distinguish between segwit outputs that it generated addresses for
+     * and wanted to receive payments from, and segwit outputs that it never
+     * generated addresses for, but it could spend just because of having keys.
+     * (Before segwit activation it was also important to not treat segwit
+     * outputs to arbitrary wallet keys as payments, because these could be
+     * spent by anyone without even needing to sign with the keys.)
+     *
+     * Some of the scripts stored in mapScripts are memory-only and
+     * intentionally not saved to disk. Specifically, scripts added by
+     * ImplicitlyLearnRelatedKeyScripts(pubkey) calls are not written to disk so
+     * future wallet code can have flexibility to be more selective about what
+     * transaction outputs it recognizes as payments, instead of having to treat
+     * all outputs spending to keys it knows as payments. By contrast,
+     * mapScripts entries added by AddCScript(script),
+     * LearnRelatedScripts(pubkey, type), and LearnAllRelatedScripts(pubkey)
+     * calls are saved because they are all intentionally used to receive
+     * payments.
+     *
+     * The FillableSigningProvider::mapScripts script map should not be confused
+     * with LegacyScriptPubKeyMan::setWatchOnly script set. The two collections
+     * can hold the same scripts, but they serve different purposes. The
+     * setWatchOnly script set is intended to expand the set of outputs the
+     * wallet considers payments. Every output with a script it contains is
+     * considered to belong to the wallet, regardless of whether the script is
+     * solvable or signable. By contrast, the scripts in mapScripts are only
+     * used for solving, and to restrict which outputs are considered payments
+     * by the wallet. An output with a script in mapScripts, unlike
+     * setWatchOnly, is not automatically considered to belong to the wallet if
+     * it can't be solved and signed for.
+     */
     ScriptMap mapScripts GUARDED_BY(cs_KeyStore);
 
     void ImplicitlyLearnRelatedKeyScripts(const CPubKey& pubkey) EXCLUSIVE_LOCKS_REQUIRED(cs_KeyStore);
diff --git a/src/wallet/scriptpubkeyman.cpp b/src/wallet/scriptpubkeyman.cpp
index 4c9d88973..0c95ab29b 100644
--- a/src/wallet/scriptpubkeyman.cpp
+++ b/src/wallet/scriptpubkeyman.cpp
@@ -70,7 +70,15 @@ bool HaveKeys(const std::vector<valtype>& pubkeys, const LegacyScriptPubKeyMan&
     return true;
 }
 
-IsMineResult IsMineInner(const LegacyScriptPubKeyMan& keystore, const CScript& scriptPubKey, IsMineSigVersion sigversion)
+//! Recursively solve script and return spendable/watchonly/invalid status.
+//!
+//! @param keystore            legacy key and script store
+//! @param script              script to solve
+//! @param sigversion          script type (top-level / redeemscript / witnessscript)
+//! @param recurse_scripthash  whether to recurse into nested p2sh and p2wsh
+//!                            scripts or simply treat any script that has been
+//!                            stored in the keystore as spendable
+IsMineResult IsMineInner(const LegacyScriptPubKeyMan& keystore, const CScript& scriptPubKey, IsMineSigVersion sigversion, bool recurse_scripthash=true)
 {
     IsMineResult ret = IsMineResult::NO;
 
@@ -129,7 +137,7 @@ IsMineResult IsMineInner(const LegacyScriptPubKeyMan& keystore, const CScript& s
         CScriptID scriptID = CScriptID(uint160(vSolutions[0]));
         CScript subscript;
         if (keystore.GetCScript(scriptID, subscript)) {
-            ret = std::max(ret, IsMineInner(keystore, subscript, IsMineSigVersion::P2SH));
+            ret = std::max(ret, recurse_scripthash ? IsMineInner(keystore, subscript, IsMineSigVersion::P2SH) : IsMineResult::SPENDABLE);
         }
         break;
     }
@@ -147,7 +155,7 @@ IsMineResult IsMineInner(const LegacyScriptPubKeyMan& keystore, const CScript& s
         CScriptID scriptID = CScriptID(hash);
         CScript subscript;
         if (keystore.GetCScript(scriptID, subscript)) {
-            ret = std::max(ret, IsMineInner(keystore, subscript, IsMineSigVersion::WITNESS_V0));
+            ret = std::max(ret, recurse_scripthash ? IsMineInner(keystore, subscript, IsMineSigVersion::WITNESS_V0) : IsMineResult::SPENDABLE);
         }
         break;
     }
@@ -476,11 +484,11 @@ std::unique_ptr<SigningProvider> LegacyScriptPubKeyMan::GetSigningProvider(const
 
 bool LegacyScriptPubKeyMan::CanProvide(const CScript& script, SignatureData& sigdata)
 {
-    if (IsMine(script) != ISMINE_NO) {
-        // If it IsMine, we can always provide in some way
-        return true;
-    } else if (HaveCScript(CScriptID(script))) {
-        // We can still provide some stuff if we have the script, but IsMine failed because we don't have keys
+    IsMineResult ismine = IsMineInner(*this, script, IsMineSigVersion::TOP, /* recurse_scripthash= */ false);
+    if (ismine == IsMineResult::SPENDABLE || ismine == IsMineResult::WATCH_ONLY) {
+        // If ismine, it means we recognize keys or script ids in the script, or
+        // are watching the script itself, and we can at least provide metadata
+        // or solving information, even if not able to sign fully.
         return true;
     } else {
         // If, given the stuff in sigdata, we could make a valid sigature, then we can provide for this script
diff --git a/src/wallet/test/scriptpubkeyman_tests.cpp b/src/wallet/test/scriptpubkeyman_tests.cpp
new file mode 100644
index 000000000..757865ea3
--- /dev/null
+++ b/src/wallet/test/scriptpubkeyman_tests.cpp
@@ -0,0 +1,43 @@
+// Copyright (c) 2020 The Bitcoin Core developers
+// Distributed under the MIT software license, see the accompanying
+// file COPYING or http://www.opensource.org/licenses/mit-license.php.
+
+#include <key.h>
+#include <script/standard.h>
+#include <test/util/setup_common.h>
+#include <wallet/scriptpubkeyman.h>
+#include <wallet/wallet.h>
+
+#include <boost/test/unit_test.hpp>
+
+BOOST_FIXTURE_TEST_SUITE(scriptpubkeyman_tests, BasicTestingSetup)
+
+// Test LegacyScriptPubKeyMan::CanProvide behavior, making sure it returns true
+// for recognized scripts even when keys may not be available for signing.
+BOOST_AUTO_TEST_CASE(CanProvide)
+{
+    // Set up wallet and keyman variables.
+    NodeContext node;
+    std::unique_ptr<interfaces::Chain> chain = interfaces::MakeChain(node);
+    CWallet wallet(chain.get(), WalletLocation(), WalletDatabase::CreateDummy());
+    LegacyScriptPubKeyMan& keyman = *wallet.GetOrCreateLegacyScriptPubKeyMan();
+
+    // Make a 1 of 2 multisig script
+    std::vector<CKey> keys(2);
+    std::vector<CPubKey> pubkeys;
+    for (CKey& key : keys) {
+        key.MakeNewKey(true);
+        pubkeys.emplace_back(key.GetPubKey());
+    }
+    CScript multisig_script = GetScriptForMultisig(1, pubkeys);
+    CScript p2sh_script = GetScriptForDestination(ScriptHash(multisig_script));
+    SignatureData data;
+
+    // Verify the p2sh(multisig) script is not recognized until the multisig
+    // script is added to the keystore to make it solvable
+    BOOST_CHECK(!keyman.CanProvide(p2sh_script, data));
+    keyman.AddCScript(multisig_script);
+    BOOST_CHECK(keyman.CanProvide(p2sh_script, data));
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/test/functional/feature_backwards_compatibility.py b/test/functional/feature_backwards_compatibility.py
index 1ac10f971..7a6e3df70 100755
--- a/test/functional/feature_backwards_compatibility.py
+++ b/test/functional/feature_backwards_compatibility.py
@@ -122,6 +122,9 @@ class BackwardsCompatibilityTest(BitcoinTestFramework):
         info = wallet.getwalletinfo()
         assert info['private_keys_enabled']
         assert info['keypoolsize'] > 0
+        # Use addmultisigaddress (see #18075)
+        address_18075 = wallet.addmultisigaddress(1, ["0296b538e853519c726a2c91e61ec11600ae1390813a627c66fb8be7947be63c52", "037211a824f55b505228e4c3d5194c1fcfaa15a456abdf37f9b9d97a4040afc073"], "", "legacy")["address"]
+        assert wallet.getaddressinfo(address_18075)["solvable"]
 
         # w1_v18: regular wallet, created with v0.18
         node_v18.createwallet(wallet_name="w1_v18")
@@ -319,7 +322,7 @@ class BackwardsCompatibilityTest(BitcoinTestFramework):
         hdkeypath = info["hdkeypath"]
         pubkey = info["pubkey"]
 
-        # Copy the wallet to the last Bitcoin Core version and open it:
+        # Copy the 0.17 wallet to the last Bitcoin Core version and open it:
         node_v17.unloadwallet("u1_v17")
         shutil.copytree(
             os.path.join(node_v17_wallets_dir, "u1_v17"),
@@ -331,5 +334,14 @@ class BackwardsCompatibilityTest(BitcoinTestFramework):
         descriptor = "wpkh([" + info["hdmasterfingerprint"] + hdkeypath[1:] + "]" + pubkey + ")"
         assert_equal(info["desc"], descsum_create(descriptor))
 
+        # Copy the 0.19 wallet to the last Bitcoin Core version and open it:
+        shutil.copytree(
+            os.path.join(node_v19_wallets_dir, "w1_v19"),
+            os.path.join(node_master_wallets_dir, "w1_v19")
+        )
+        node_master.loadwallet("w1_v19")
+        wallet = node_master.get_wallet_rpc("w1_v19")
+        assert wallet.getaddressinfo(address_18075)["solvable"]
+
 if __name__ == '__main__':
     BackwardsCompatibilityTest().main()